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. --^ 



VALVE-GEARS 



FOR 



STEAM-ENGINES. 



BY 

CECIL H. PEABODY, 

ASSOCIATE PROFESSOR OF STEAM-ENGINEERING AT THE MASSACHUSETTS 
INSTITUTE OF TECHNOLOGY. 



NEW YORK: 

JOHN WILEY & SONS, 

53 East Tenth Street. 

1892. 









^^ 






Copyright, i8q2. 

BV 

CECIL H. PEABODY. 



■Robert DuuMHOin>, 

Electrotyper, 

iAi &i46 Pearl Street, 

New York. 




Febsis Bros., 
Printers, 

S26 Peaxl Streefi»» 
New York, 



PREFACE. 



This book is intended to give engineering students instruc- 
tion in the theory and practice of designing valve-gears for 
steam-engines. With the vast number of valves and gears in 
use at the present time, an exhaustive treatment in a text- 
book appears out of place ; the author's aim is rather to give 
the learner a firm, grasp of the principles and some facility in 
their application. Each type discussed is illustrated by one or 
more examples selected from good practice. 

In the presentation of the elementary principles, geometri- 
cal or analytical methods are used as necessity or convenience 
may suggest ; but in the application, geometrical methods are 
used exclusively, in conformity with the usual and preferable 
habit of laying out valve-gears by construction. Zeuner's 
valve-diagram is used because it is widely and favorably known 
and appears to the author to be at least as good as any other 
circular diagram. 

In the discussion of radial valve-gears, ^he underlying 
Drinciples found in all such gears are pointed out, and a few 
prominent forms are illustrated. All such gears have neces- 
sarily or designedly large irregularities in their motions, so that 
analytical methods are useless if not misleading, and general 
methods of treatment are of small value. Facility in design is 
to be obtained through experience only. 



ill 



IV PREFA CE. 

Drop cut-off gears are represented by a few examples chosen 
to illustrate the principles and show a variety of treatment ; 
especial attention is given to the Corliss gear. Advantage is 
taken in this connection of the opportunity to illustrate the 
use of cam-gears. 

Common and well-known methods and processes have been 
used in most cases, and novelty has been rather avoided than 
sought. Some things, however, are believed to be here pre- 
sented for the first time ; for example, the combination of a 
skeleton model with construction for laying out link-motions 
and other irregular or complicated gears, and several examples 
of double valve-gears ; the latter are introduced mainly to show 
the scope of the methods used. So much of the material used 
is the accumulation of common practice, and so many of the 
forms and methods are known by the names of the originators, 
that references to authorities or formal acknowledgments ap- 
pear superfluous. 

C. H. P. 

Massachusetts Institute of Technology, 
March, 1892. 



\ 



TABLE OF CONTENTS. 

PAGE 

CHAPTER I. 
Plain Slide-valve, . i 

CHAPTER II. 
Shifting Eccentrics, 33 

CHAPTER III. 
Link-motions, 39 

CHAPTER IV, 
Radial Valve-gears, 88 

CHAPTER V. 
Double Valve-gears, 97 

CHAPTER VI. 
Drop Cut-off Valve-gears, 115 

V 



VALVE-GEARS FOR STEAM-ENGINES. 



CHAPTER I. 
PLAIN SLIDE-VALVE. 

The valve-gear of a steam-engine consists of the valve, or 
valves, for adnnitting steam to, and exhausting steam from, the 
cylinder of the engine, together with the mechanism for giving 
motion to the valve, or valves. The discussion of valve-gears 
is therefore a part of kinematics or mechanism ; the extent and 
importance of the subject make a separate presentation of it 
desirable. 

The larger part of valve-gears derive their motion from one 
or more eccentrics ; of such gears, the plain slide-valve is the 
simplest. Other valve-gears are best studied after an exami- 
nation of the plain slide-valve, since they accomplish the same 
results, and by analogous methods. 

Slide-valve Engine. — The working parts of a plain slide- 
valve engine are shown by Fig. i, PL I ; the frame is omitted 
in order that those parts may be the more readily understood. 
The centre of the main shaft is at 6^ ; the crank-pin is at C; 
the centre of the eccentric is at £ ; Z is the connecting-rod, 
joining the crank-pin to the cross-head at //; / is the eccentric- 
rod, joining the eccentric to the head /i of the valve-spindle. 
Both cross-head and valve-spindle head are constrained by 



2 VALVE-GEARS FOR STEAM-ENGINES. 

guides to move in a line parallel to the axis of the cylinder. 
The steam-chest is represented with the cover off, to show the 
valve and its seat ; the upper part of the valve is cut away to 
show the steam-ports and the exhaust-space. Fig. 2 gives a 
section of the valve and a half-section of the cylinder, with the 
piston P near the beginning of the stroke, and with the valve 
F partially open. The section being through the centre of the 
valve-spindle, the form of the exhaust-cavity is partially ob- 
scured. Fig. 3 gives a clearer idea of the valve and its seat. 

Crank and Connecting-rod. — The crank, connecting-rod, 
and cross-head, in its guides, form what is called a slider-crank 
train, more clearly represented by OCH, Fig. 4. 

Let the length of the connecting-rod be represented by Z, 
the length of the crank by R, and the angle which the crank 
makes with the centre line XX', by 6 ; then the displacement 
HA of the cross-head from the beginning of its stroke is ; 



D=OA-Oc -{HC - CcJ ; 

D =^ L-\- R- RcosO ^ {U - R' sin' 6)^ ; 

In designing valve-gears, it is more convenient, and suffi- 
ciently accurate, to find the displacement of the piston for a 
given crank-angle by the construction shown by Fig. 4. The 
converse of this, i.e. to find the crank-angle corresponding to a 
given piston-position, is found with equal facility by such a 
construction, while the calculation by aid of equation (i) is 
troublesome. The principal use of that equation is in study- 
ing the nature of the irregularity introduced by the connect- 
ing-rod into the motion of the cross-head, and for that purpose 
it is convenient to expand the expression containing L by the 




PLAIN SLIDE-VALVE. 3 

binomial theorem, rejecting terms having the higher powers 
of L in the denominator ; whence 

D=R{\-co^e)-\-L\ I - (i - 

T\ r^f a\ \ ^ sin' d 

n = R{i- COS 6)+ ^^ (2) 

The ratio of crank to connecting-rod in stationary-engine 
practice varies from i : 5 to i : 7^^. In marine engineering the 
ratio I : 4, or even more, sometimes obtains. The maximum 
value of the term containing L occurs at ^ = 90° ; for the 
ratios of crank to connecting-rod just given, the term containing 
L has then the values -^^R, -^jR, ^R, respectively. It is appar- 
ent that the difference between the motion of the cross-head 
and piston, and harmonic motion represented by the equation 

D ^ R {1 - cos 6), (3) 

is always notable, and may be large. 

Eccentric and Eccentric-rod. — The eccentric is derived 
from the crank, by the expansion of the crank-pin till it in- 
cludes the shaft and obliterates the crank. Consequently the 
eccentric and eccentric-rod form a slider-crank train. The dis- 
placement of the valve is always reckoned from the middle 
position, and in Fig. 4 is ^ = ^^2: ; it may be calculated as fol- 
lows : 

e = Oe+Oa-{£k' - £7)^; 

,'.e = r cos{90° -{0 + ^)\+^- U'- r'sm'{go°- {6 +d)}]^ ; 

• /zi , ^x , /f i r'cos»(^+<^)H1 , X 

,-. ^ = rsm(^+d) + /|^i -| I _^_^|J. . . (4) 



4 VALVE-GEARS FOR STEAM-ENGINES. 

This equation differs from equation (i) only in that the 
eccentric-angle and the valve-displacement are reckoned from 
different points. Expanding by the binomial theorem and 
rejecting terms containing the higher powers of / in the denom- 
inator gives 

• (f^\ ,, , r^cos''(^ + <y) , . 

The length of the eccentric-rod is commonly from 12 to 2a 
times the eccentricity ; the right-hand term for such ratios will 
have the values -^^r and :^^r, respectively, for maxima. It is 
customary to assume the motion of the valve to be harmonic^ 
in which case it is represented by the equation 

e=rsin{6-\-6) (6) 

The error of this assumption, though appreciable, is not 
large; moreover the method of setting valves of engines pre- 
vents any inconvenience from this source unless the eccentric- 
rods are very short. 

The Slide-valve. — Fig. 3 gives the section of a plain slide- 
valve and its seat. The por^s a,a^ lead to the two ends of the 
cylinder ; the exhaust-space s is connected with the exhaust- 
pipe ; the bridges b, b^ separate the ports from the exhaust- 
space. The steam-pressure in the steam-chest holds the valve 
against the seat and prevents leakage. The valve-seat is cut 
away so that the valve may over-travel its seat at the ends and 
thus both valve and seat may wear evenly. The edges of the 
ports and of the valves are machined and finished true ; for 
convenience in the work, the edges of the ports and the inside 
edges of the valve are undercut as shown. 

The valve commonly overlaps both inside and outside edges 
of the ports. The amount, o^ by which the valve laps over the 
outside edge of the port is called the outside lap of the valve ; 



PLAIN SLIDE-VALVE. 5 

in like manner, / is called the inside lap. Frequently the outside 
lap is called simply the lap. In the figure the laps are equal ; 
in some cases they are unequal. The inside lap may be noth- 
ing, or negative, in which case the valve is said to have a 
clearance. 

In Fig. 2 the valve is shown admitting steam to the end of 
the cylinder remote from the crank, called the head end ; 
and it is exhausting steam from the other end of the cylinder,, 
called the crank end. The valve is set in such a manner that 
when the engine is on a dead-point the valve is open by a small 
amount called the lead. For this purpose the eccentric is set 
ahead of the crank 90° plus the angle d", called the angular 
advance. As the crank moves forward the valve opens more 
and more till the centre of the eccentric comes to the line of 
centres, then the valve begins to return and it shuts the port 
before the stroke of the piston is finished. The stroke from 
the head to the crank end is called the forward stroke ; the 
return stroke is made from the crank to the head end. The 
valve is open by the amount of the lead at the beginning of 
the return stroke, and at the same time the exhaust is open for 
the head end. As in the forward stroke, the valve first opens 
wider as the stroke proceeds, then it returns and closes the port 
before the piston reaches the end of the stroke. 

Events of the Stroke. — When the outside edge of the 
valve is at the edge of the port, as shown by Fig. 4, PI. II, 
and the valve is opening, admission is said to occur. This 
happens just before the stroke commences. When the valve 
is in the same position, but is closing, cut-off takes place. At 
either position the displacement of the valve is equal to the 
outside lap ; consequently we have the following principle : 

When the displacement of the valve is equal to the outside lapy 
the engine is either at admission or cut-off. 

Release occurs when the inside edge of the valve is at the 
edge of the port and the valve is opening to exhaust, as shown 
by Fig. 5, PL II. 



D VALVE-GEARS FOR STEAM-ENGINES. 

Compression occurs when the valve is at the same position 
but is closing the exhaust. At either position the displace- 
ment of the valve is equal to the inside lap ; consequently we 
have : 

When the displacement of the valve is equal to the inside lap^ 
the engine is either at release or at co^npression. 

Valve-ellipse. — The action of the valve is conveniently 
studied by the aid of a diagram like that shown by Fig. i, PI. 
II, and known as a valve-ellipse. It is obtained by laying off 
the displacements of the piston {HA, Fig. 4, PI. I) as abscis- 
sae, and the displacements of the valve {ha, Fig. 4, PI. I) as 
ordinates, for a sufficient number of crank-positions, and by 
drawing a smooth curve through the points thus found. Any 
convenient scale may be used for either abscissae or ordinates ; 
in practice the ordinates may be full scale, while the abscissae 
are quarter scale or less. In the figure the abscissae are made 
equal to the displacements of the piston from Fig. 4, PI. I, and 
the ordinates are made twice the valve-displacements from the 
same figure. 

The figure is properly an oval on account of the influence 
of both connecting-rod and eccentric-rod. The dotted ellipse 
is drawn to show the irregularities, which are large in the figure 
on account of the unfavorable ratios of crank to connecting-rod, 
and of eccentric to eccentric-rod, in Fig. 4, PI. I. 

The lines 00', o^o^ are drawn parallel to AA', and at a dis- 
tance Ao = Ao^ equal to the outside lap ; and the lines ii', ij,^ 
are at a distance Ai = Ai^ equal to the inside lap. Now a 
displacement of the valve equal to the outside lap will give 
either admission or cut-off ; an inspection of the diagram shows 
that admission occurs at 0.02 of the stroke before the dead- 
point, and that cut-off occurs at 0.88 of the stroke, for the for- 
ward stroke ; for the return stroke, the admission occurs just 
before the dead-point, and cut-off occurs at 0.72 of the stroke. 
Compression occurs at 0.94 and release at 0.98 of the stroke, 
for the forward stroke ; and for the return stroke compression 



PLAIN SLIDE-VALVE. 7 

occurs at 0.83 and release at 0.93 of the stroke. The lead for 
the forward stroke is on, and for the return stroke o^n' . The 
inequaHty of the leads is due to the short eccentric-rod ; in 
practice such an inequality does not occur, first, because the 
eccentric-rod is longer, and second, because the usual method 
of setting the valve makes the lead equal. 

The valve-ellipse may be advantageously used to investio-ate 
the action of a valve having an irregular motion, such as is 
given by some special valve-gears to be studied later, and it 
should be drawn during the design of the valves for every 
important engine. The motion of valves of an existing engine 
may be investigated by causing the engine to draw its own 
valve-ellipse. For this purpose, a reduced copy of the piston- 
motion, obtained by aid of a pantograph or otherwise, may be 
communicated to a slip of paper on which is pressed a pencil 
that derives its motion across the slip of paper from the valve- 
gear. The oval thus drawn will have the piston-displacements 
for abscissae and the valve-displacements for ordinates, and 
should be identical with the valve-ellipse drawn to the same 
scale ; any discrepancy must be due to mechanical defects in 
the valve-gear. 

* Sinusoidal Diagram. — A diagram called by this name, be- 
cause the curves resemble sinusoids, was devised by Moll and 
Montety for use in designing valve-gears, taking account of the 
irregularities of both the piston and the valve. Starting at A, 
Fig. 2, the crank-angles are laid ofT as abscissae toward A" ; and 
both the piston-displacement and the valve-displacement for 
a given crank-angle are laid off as ordinates, thus giving two 
curves, ^^'^'^'^ representing the piston-motion, and nn'n, rep- 
resenting the valve-motion. The dotted lines are true sinus- 
oids, and would represent the piston and valve motions if both 
were harmonic. The lines 00' 0, o^o^o^ are drawn to represent 
the outside laps, and the lines ii'i, ij^'i^ to represent the inside 
laps, which may or may not be equal. Inspection of the dia- 
gram shows that cut-off occurs at the crank-angle 133°, and at 



8 VALVE-GEARS FOR STEAM-ENGINES. 

a piston displacement equal to ab. Conversely, if the cut-off is 
desired to take place at the piston-position ab, draw the line 
b'b" parallel to A A" and at a distance from it equal to the 
desired piston-displacement ; from b, the intersection with the 
curve of piston-displacements, draw the ordinate ab ; then ac 
is the lap which will give the desired cut-off. It is convenient 
to draw the curve of piston-displacements on a sheet of paper 
on a drawing-board, and to draw the curve of valve-displace- 
ments, which may be extended to give about one and a half 
revolutions, on a piece of tracing-paper or tracing-cloth. By 
superimposing the tracing of the valve-displacements on the 
drawing of the piston-displacements, and slipping it along as 
desired, the effect of using different values for the angular 
advance may be readily determined ; at the same time the 
effect of different laps may be determined, or the lap for a 
special purpose may be found. 

This diagram cannot be conveniently substituted for the 
valve-ellipse, since it does not present to the eye the character 
of the valve-motion combined with the piston-motion ; a valve- 
ellipse can readily be drawn from the sinusoidal diagram. 

Zeuner's Diagram. — Fig. 7 shows a diagram devised by 
Zeuner for investigating the action of, and for designing, valves 
which have harmonic motion. Let XOX' and 6^F be a pair 
of rectangular axes, and let the crank have a left-handed rota- 
tion as shown by the arrow. Lay off the angle YOP := S equal 
to the angular advance, toward the crank ; make OP equal to 
the eccentricity, and on it draw a circle ONP called the valve- 
circle ; then the valve-displacement for a given crank-angle is 
equal to the chord ON, cut off by the valve-circle from the line 
representing the crank. To prove this, we have Op for the 
position of the eccentric corresponding to the crank-position 
ORy obtained by making the angle /6^i? equal to 90° -|- S ; and 
we have On for the valve-displacement on the assumption of 
harmonic motion, and 



PLAIN SLIDE-VALVE, g 

On — r cos>pOn — r cos (i8o° — 90° — 6 — d) = e\ 
.*. e = rsm{d -\- 6\ 

as given by equation (6). But the triangles Opn and OPN are 
equal, since they are right-angled triangles with the sides Op 
and OP equal, and the angles PON and pOn are each equal to 
180° - 90° - 6/ - d. 

The use of the diagram is shown by Fig. i, PL III. Two 
valve-circles are drawn, OP for the forward and OP' for the 
return stroke. The circles oo'o" and ii'i'', drawn with the out- 
side and inside laps as radii, are called the lap-circles. At the 
beginning of the stroke the valve-displacement is On = Oo 
-\- on, and the lead is on ; the valve is in the position shown by 
Fig. 3, PI. II. As the crank moves forward the valve opens, 
at first rapidly, and then more slowly, till the maximum dis- 
placement is attained, when the crank coincides with 0P\ the 
position of the valve is then shown by Fig. 6, PI. II. As the 
crank moves beyond the last position the valve returns, till at 
ORc the displacement is equal to the lap and cut-off occurs ; 
the position of the valve is then shown by Fig. 4, PI. II, and 
it is moving toward the right to shut the port. At ORk the 
displacement of .the valve is equal to the inside lap and com- 
pression occurs; the position of the valve is shown by Fig. 5, 
PI. II, and it is moving toward the right to shut the exhaust- 
port. At ORr the displacement of the valve is again equal to 
the inside lap and release occurs ; the valve now has the left- 
hand inside edge on the edge of the port and it is moving to 
open the port. At ORJ the displacement of the valve is equal 
to the outside lap and admission occurs at the crank end ; the 
position of the valve to give admission at the head end (cor- 
responding to the crank-position OR^ is shown by Fig. 4, PI. 
II. It is customary to associate the admission at OR^, in 
anticipation of the forward stroke, with that stroke, and to 
associate the admission at ORJ with the return stroke. 



lO VALVE-GEARS FOR STEAM-ENGINES. 



' jr 



Though it is not customary to do so, the two arcs tt t'\ ss s 
may be added to find the crank-positions at which the edge of 
the valve is on the further edge of the port, and the port is 
wide open. The radius Ot' is made equal to the width of the 
port plus the outside lap ; when the crank-position passes 
through / or t" the displacement of the valve is equal to 
the lap plus the width of the port and the port is then wide 
open. In like manner the radius Os' is made equal to the 
width of the port plus the inside lap, and when the crank-posi- 
tion passes through s or s^' the port is wide open for exhaust. 

The diagram shows that the outside edge of the valve over- 
travels the edge of the port by the amount t'P. Some over- 
travel is desirable to give a free flow of steam to the cylinder 
and a rapid admission and a sharp cut-off. The over-travel of 
the valve for exhaust is s'P, which is greater than t'P by the 
amount of the difference of the outside and inside laps. The 
amount by which the port is open at any position of the valve 
is called the port-opening. The maximum port-opening for 
supply, which occurs when the crank coincides with OP, is 
equal to o'P, the difference between the eccentricity and the 
lap. The maximum port-opening for exhaust is equal to i'P. 
A slide-valve moved by an eccentric always has the maximum 
port-opening for exhaust at least as great as the width of the 
port, and it is commonly greater; the maximum port-opening 
for supply is also commonly greater than the width of the port, 
but it is sometimes less. A slide-valve moved by a gear that 
gives a variable cut-off, as will be seen later, may have both 
maximum port-openings less than the width of the port for 
some settings of the gear. 

An inspection of the diagram Fig. i, PI. Ill, will show that 
a change of the outside lap will affect both admission and cut- 
off ; thus, the cut-off is hastened and the admission is delayed 
by an increase of the outside lap, and conversely the admission 
comes earlier and the cut-off comes later if the outside lap is 
decreased. In a similar way, increasing the inside lap delays 



PLAIN SLIDE-VALVE. II 

the release and hastens the compression, while decreasing that 
lap produces a contrary effect. Since it is the relative propor- 
tions of lap and eccentricity which determine the cut-off, it is 
apparent that decreasing the eccentricity with a constant lap 
produces the same effect as increasing the lap with a constant 
eccentricity ; i,e. it hastens the cut-off and delays the admis- 
sion. Finally, it will be seen that increasing the angular 
advance hastens all the events of the stroke ; and that decreas- 
ing the angular advance delays all the events of the stroke. 

Should the inside lap be made nothing, so that in mid-gear 
the inside edge of the valve shall coincide with the edge of the 
port, then both compression and release will occur when the 
crank is at right angles to POP' . Sometimes, in designing or 
remodelling a valve, it will be found advisable to give a clear- 
ance to the valve instead of an inside lap, in which case the 
engine will for a short time, near the end of the stroke, ex- 
haust from both ends at once. Suppose that the circle ii'i'\ 
Fig. I, PI. Ill, represents a clearance, then release will occur 
at ORk and compression at OR,.. 

Expansion and Compression. — From cut-off at OR, (Fig. 
I, PI. Ill) to release at OR^-, the head end of the cylinder is 
shut off from both the supply and the exhaust. While the 
crank moves forward from R, to R^ the piston moves a corre- 
sponding amount, and the steam in the cylinder expands and 
experiences a loss of pressure in consequence ; this action is 
called the expansion. When the valve closes the exhaust at 
ORk the steam then caught in the cylinder is compressed 
ahead of the piston till a new supply of steam is admitted at 
ORJ ; this action is called the compression. On the return 
stroke, in a like manner, steam is expanded from OR, to ORJ, 
and is compressed from ORk to OR^- 

Rocker and Bell-crank Lever. — In the work thus far it 
has been assumed that the centre-lines of the crank and con- 
necting-rod with the cross-head and piston, and of the eccentric 
and eccentric-rod with valve-spindle and valve, coincide in the 



12 VALVE-GEARS FOR STEAM-ENGINES. 

elevation, as shown by Fig. i, PI, I. This assumption is con- 
venient in giving the first description of the valve-gear and in 
discussing the action and the theory of the valve-motion ; and 
the design of the valve is commonly carried on as though such 
a coincidence existed, the deviation from such a coincidence 
being considered only in the mechanical problem of laying out 
the mechanism of the engine. 

If the centre-line of the valve-spindle passes through the 
centre of the shaft, and the eccentric-rod is connected directly 
to the valve-spindle, then the motion of both crank and con- 
necting-rod, and eccentric and eccentric-rod, referred to their 
own proper axes, will be the same as already found, even 
though their centre-lines do not coincide. Such a lack of co- 
incidence will make the angle between the eccentric and the 
crank more (or less) than 90° plus the angular advance, by the 
amount of the angle between the two centre-lines. This dif- 
ference needs consideration only in the process of setting the 
valve ; and if the angle between the centre-lines is small, it will 
require little or no attention at that time. Since such an 
arrangement involves a lack of parallelism between the paths 
of the valve and of the piston, the work of boring thecylin- 
der and facing off the valve-seat is more troublesome, and other 
machine-work is more difficult, unless special processes are pro- 
vided ; consequently this arrangement is seldom adopted. 

Very commonly the paths of the piston and the valve are 
parallel but do not coincide in the elevation ; thus, the axis of 
the crank and connecting-rod with the cross-head and cylinder 
may be XX' in the Figs. 2, 3, and 4, PI. Ill, while the centre- 
line of the valve-spindle may be xx' in the same figures. In 
such cases a rocker or a bell-crank lever should be used to 
transmit motion from the eccentric to the valve. 

The following method may be used in laying out a bell- 
crank lever. Let A be the position of the end of the valve- 
spindle when the valve is in mid-position ; lay off Aa = Aa' 
equal to the lap of the valve, and with a radius equal to the 



PLAIN SLIDE-VALVE. 1 3 

length of the arm of the bell-crank lever draw arcs intersecting 
at C\ this gives the axis about which the bell-crank lever 
vibrates. This construction prevents the bell-crank lever from 
introducing any irregularity into the action of the valve at 
admission and cut-off; irregularities at other times are of less 
consequence. In laying out such a gear for a locomotive with 
a rigid valve-spindle that extends directly from the end of the 
bell-crank lever or rocker to the valve-yoke, it is important to 
have the bending or lateral motion of the valve-spindle as small 
as possible ; in such case the point C may be so chosen that 
the lateral motion of the end of the valve-spindle shall be half 
above and half below the line xx' . With a radius equal to BC^ 
the other arm of the bell-crank lever, draw an arc as shown, 
and draw a tangent to this arc from O. Draw perpendiculars 
OE and CB from O and C to this tangent ; then EB is the 
length of the eccentric-rod. If desired, the relation of the 
crank and eccentric may be found by laying off the angle 
XOR = ^, the angular advance, since the crank is at that 
angle before the dead-point when the valve is in mid-position ; 
the angle EOR will not be equal to 90° -f- S, but this is a 
matter that affects the valve-setting only, and even in that 
process the exact knowledge of the angle between the crank 
and eccentric is not of importance. 

If it is considered of importance that the eccentric-rod shall 
be some definite length, then the centre C, on which the bell- 
crank lever vibrates, may be shifted so as to give that length. 
If C is to be shifted a short distance, then a line parallel to XX^ 
may be drawn through B, and with a radius equal to the desired 
length of the eccentric-rod an arc may be drawn from E inter- 
secting that parallel line at a point B^ ; the whole bell-crank 
lever is to be shifted bodily to the extent BB\ and the length 
of the valve-spindle must be changed the same amount. 

In the figure the arm CB is made J of CA ; consequently 
the motion of the valve will be that which would be given by 
an eccentric equal to f of OE if the connection were direct. 



14 VALVE-GEARS FOR STEAM-ENGINES. 

In designing and laying out the valve it is treated as though it 
were moved by such an eccentric. The ratio of the arms may 
be made anything desired ; they have commonly the same 
length. 

In laying out a rocker, the process is the same as that just 
described for the bell-crank lever, except that the arm CB, Fig. 
3, is laid off on the side opposite A, and the eccentric follows 
the crank. 

Fig. 4 shows the equal-armed straight rocker with the centre 
of vibration C midway between the lines XX' and xx' ; it may 
be made a little longer so as to give a construction equivalent 
to that shown by aAa' , Figs. 2 and 3. 

Area of Steam-pipe and Steam-ports. — In order that the 
loss of pressure in the steam-pipe due to friction may not be 
excessive, it is customary to limit the velocity to 100 feet a 
second or 6000 feet per minute. The volume of steam supplied 
to an engine is calculated, for this purpose, on the assumption 
that the cylinder is filled at each stroke. 

For example, the diameter of the steam-pipe of an engine 
having a diameter of 18 inches and a stroke of 3 feet, and 
making 75 revolutions per minute, should be 5 inches. It 
may be found as follows : The piston displacement is 

7r/i8\2 

\^) X 3 = 17671 X 3 = 5-30 cubic feet; 

the volume of steam per second is 

7c 
2 X 5.30 X ^ = 13.25 cubic feet; 

the area of the steam-pipe should be 
13.25 



100 



X 144 = 19.08 square inches, 



PLAIN SLIDE-VALVE. 1 5 

and the diameter should be 



X 19.08) = 4.93 inches, 

or nearly 5 inches. 

Even though the cut-off occurs before the end of the stroke 
and the actual volume of steam used is less than the volume 
calculated by the above method, the area of the steam-pipe 
should not be reduced, for the rate of the flow of steam will 
be as great when the piston is near mid-stroke. The steam- 
pipe supplying an engine which has an early cut-off (one third 
stroke or less) may be made less than given by the above 
method, provided there is a large steam-chest, or a steam-drum 
near the engine. Seaton * states that a velocity of 8000 feet 
may be allowed in the steam-pipe of a marine engine; and 
that 10,000 feet may be allowed for very large engines. 

The area of ports and passages leading to the cylinder 
should be equal to that of the steam-pipe ; and the area of 
ports and passages leading from the cylinder should be double 
that area. If the steam-pipe is calculated on the assumption 
of a velocity of 6000 feet a minute, this rule will often make 
the size of ports and passages such that it is dif^cult, if not 
impossible, to provide for them in the design of a high-speed 
engine. In such case the area of ports and passages must be 
reduced, but they should never be less than half the area given 
by that rule. This is equivalent to calculating the area of a 
steam-port by the method given for a" steam-pipe, except that 
a velocity of 12,000 feet a minute is allowed ; and then making 
the exhaust-passage twice that area. Since both supply and 
exhaust pass through the ports of a plain slide-valve engine, the 
area must be made sufficient for the exhaust. 

For example : the engine mentioned above should have the 
area of the port 

2 X 19.08 = 38.16 ; 
* Manual of Marine Engineering. 



l6 VALVE-GEARS FOR STEAM-ENGINES. 

and if the length of the port is made eight tenths of the diam- 
eter, or 14 inches, the port will be 

38.16 -^- 14 =r 2.65 inches. 

If the area of the port is reduced to half as much the width 
will become if inches. 

When it becomes difficult or undesirable to give the slide- 
valve sufficient motion to open the steam-port wide for the 
supply, the maximum port-opening may be made from -f^ to 
y^^ the width of the port. 

When special valve-gears are used that open the valve 
rapidly and close it promptly, the area of the ports and pass- 
ages may be made smaller than the above methods provide^ 
but such reduction should be made only with complete knowl- 
edge of the action of the valve and of the effect of the reduc- 
tion of the flow of steam. 

Lead and Lead-angle. — The lead, or the amount that the 
valve is open when the engine is on a dead-point, varies with 
the type and size of the engine, from a very small amount (or 
even nothing) up to f of an inch or more. Stationary 
engines running at slow speed may have from -^-^ to -f-^ of an 
inch lead. The effect of compression is to fill the waste space 
at the end of the cylinder with steam ; consequently engines 
having much compression need less lead. Locomotive-engines 
having the valves controlled by the ordinary form of Stephen- 
son link-motion may have a small lead when running slowly 
and with a long cut-off, but when running at speed with a short 
cut-off the lead is at least J of an inch ; and locomotives that 
have a valve-gear which gives constant lead commonly have ^ 
of an inch lead. 

Zeuner's diagram does not admit of the use of the lead in 
solving problems that arise in designing valves, but we may 
use instead the lead-angle, or the angle that the crank makes 
with the line of dead-points at admission ; in Fig. i, PI. Ill, 



PLAIN SLIDE-VALVE. 1 7 

XORa is the lead-angle. The lead-angle may vary from zero 
to 8° ; a convenient lead-angle for solving problems is 2^°. 
After the required problem is solved by the aid of the lead- 
angle the conditions may be varied so as to give a desired 
lead. 

Problems on the Slide-valve. — By assuming various ele- 
ments of the valve to be known, a series of problems relating 
to the plain slide-valve may be stated and solved. Of such 
problems oite has a real importance to the designer of valve- 
gears ; others are either so simple as to require no formal solu- 
tion, or they are problems that are not likely to arise in prac- 
tice. This important problem is given below as Problem II ; 
the other, Problem I, is given as a convenient introduction to 
it, for students who here approach the subject for the first 
time. 

Problem I. Give^t the eccentricity^ the lead-angle, and the 
crank-angle at cut-off, to find the angular advance, the lap, and 
the lead. 

In Fig. I, PL IV, draw, to any convenient scale, the arc 
XR,X' to represent the path of the crank, referred to the axes 
XOX' and OY. Lay off the angle XOR^ equal to the lead- 
angle, and lay off XOR^ , the crank-angle at the point of cut-off. 
Should the piston-position at cut-off be given instead of the 
crank-angle, lay off Or, the given piston-position at cut-off, and 
draw the vertical line rR,, to find the crank-position OR^ corre- 
sponding. With equal leads and laps the crank-angle at cut-off 
will be the same for each stroke, and the mean piston-position 
will be nearly equal to the piston-position at cut-off with har- 
monic motion ; hence the above construction. 

Bisect the angle R^OR, and draw the line OP', on it draw 
the valve-circle OoPo'" , and through the intersections of this 
valve-circle by the lines ORa and OR^ draw the lap-circle 00' 0" . 
The lead is Oa. 

In Fig. I the eccentricity is \\ of an inch, the cut-off is at 
f of the stroke, and the lead-angle is 2|^°. The lap is |f of an 



1 8 VALVE-GEARS FOR STEAM-ENGINES. 

inch, and the lead is y^ of an inch ; the angular advance is 

Problem II. Given the crank-angle at cut-off, the lead-angle, 
and the maximum port-opening, to find the eccentricity, the lap, 
and the angular advance. 

As has already been stated, this problem is the one met by 
the designer in laying out a valve-gear. The angular advance 
is obtained by the same process as in Problem I ; namely, by 
bisecting the angle R^ORc- 

Now assume a trial eccentricity, preferably a little larger 
than the required eccentricity, and draw an assumed valve- 
circle OqP^ , and the corresponding lap-circle qq'q" . The 
maximum port-opening with the assumed valve-circle is q"P^ ; 
and from it the diameter of the required valve-circle, equal to 
the required eccentricity, may be obtained by the proportion 

• Assumed port-opening : actual port opening:: 

Assumed eccentricity : required eccentricity. 

A graphical solution may be made by aid of similar triangles, 
as follows : Lay off the line Oc^ = <l"P^ > in a convenient posi- 
tion, and join C^c^ ; make Oc equal to the given maximum port- 
opening, and draw cC parallel to c^C^ ; then C is the centre of 
the required valve-circle and OP is the required eccentricity. 
The lap-circle oo'o'" is drawn through the intersections of the 
valve-circle by Ra and R, . 

In Fig. 2, PL IV, the angular advance is 3iJ°, as in Fig. i ; 
the assumed eccentricity is if of an inch, which gives a port- 
opening of f|- ; the required maximum port-opening is taken 
to be f of an inch ; the required eccentricity is ly'^^ of an inch ; 
and the lead is yig- of an inch, or a trifle less. 

Modifications. — In general it is not of great importance that 
the cut-off shall occur exactly at the chosen crank-angle or 
piston-position, and it is seldom necessary to know the angular 
advance except in drawing the valve-diagram. It is, however, 
very convenient if not necessary that the lead and lap shall be 



PLAIN SLIDE-VALVE, I9 

some determined quantity stated in fractions of an inch that 
are commonly used in the machine-shop. By judicious modi* 
fications the designer may secure this for the valve without 
seriously affecting the point of cut-off. In Fig. 3, PI. IV, the 
lap, Oo^ is made f of an inch, and the lead is -^^ of an inch. At 
a the vertical aP is drawn, and from O, with a radius equal to i J 
of an inch, the vertical is intersected in P\ thus giving the 
diameter OP on which the valve-circle OaPo" is drawn. The 
cut-off comes at the crank-position OR^ , corresponding to the 
piston-position JCr instead of JC^ = f stroke, as required. 

The process of laying out a slide-valve will be considered 
in connection with the valve for equal cut-off. 

Equalization of Cut-off at the Expense of the Lead. — 
Let it be assumed that the cut-off shall occur at a given piston 
position for each stroke, taking account of the irregularity due 
to the connecting-rod. Draw the line j::X\ Fig. i, PI. V, on 
which choose for the centre of the crank and for the origin 
of coordinates, and draw the vertical axis VOY\ Draw the 
circle XVX' Y\ to any convenient scale, to represent the crank- 
circle. With a radius equal to the length of the connecting-rod, 
on the same scale, and with JC and X^ as centres, cut the centre- 
line X^x at X and x' ; this will give the stroke of the cross-head, 
equal to the stroke of the piston. Lay off the point on the 
stroke at which cut-off is to occur on both strokes, and with 
these points as centres and the length of the connecting-rod as 
a radius intersect the crank-circle at R^ and R/. In the figure 
the connecting-rod is taken to be five times the crank, and cut-off 
is assumed to occur at f of the stroke. It is at once apparent 
that the crank-angles XOR^ and X' OR^ are not equal, and 
ORc and OR^ are not one straight line. Choose a small head- 
end lead-angle XOR^\ in the figure it is 1°. Bisect the angle 
R^OR,, and draw the line POP' , on which draw the two valve- 
circles as shown. The eccentricity may be determined by a 
preliminary solution, assuming harmonic motion, as in Problem 
II, or the same solution may be made directly on the figure ; 



20 VALVE-GEARS FOR STEAM-ENGINES. 

if the latter method is used, confusion is liable to occur from 
the number of circles drawn, especially if the eccentricity is 
modified to get some convenient dimension ; consequently it is 
better to make such a construction separately and transfer the 
results to the main diagram. Draw the lap-circle oo for the 
upper valve-circle, through the intersections of that circle by 
ORa and ORc ; and draw the lap-circle o'o' for the lower valve- 
circle, through the intersection ORJ with that circle. The 
admission at ORJ occurs at the intersection of the lower valve- 
circle and the lap-circle o'o' ; the crank-end lead is large, if not 
excessive. 

It is customary, in designing a valve for equal cut-off, to 
equalize the compression also. In Fig. I the compression is 
assumed to occur at f of the stroke, or at the crank-positions 
ORk and ORk The inside laps are it and i'i', so that the 
release occurs at R^ and i?/. The point of intersection i of 
the line ORk with the valve-circle may be determined by drop- 
ping a perpendicular Pi from P on ORj,. The valve-diagram 
in Fig. I gives the following dimensions : 

Eccentricity ij inch. 

Outside lap, forward stroke -|^ *' 

return stroke f T " 

Inside lap, forward stroke tV " 

return stroke -g^^ " 

Head-end lead A " 

Crank-end lead -^1- " 

To lay out a Slide-valve. — The valve for which dimen- 
sions were found in Fig. i PL V, is shown in section by Fig. 2. 
To lay out the valve, begin at the crank end and make ab =^ ^ 
of an inch, equal to the return-stroke outside lap ; make be = r^-^ 
of an inch, equal to the width of the port. 

The greatest displacement of the valve, equal to the eccen- 
tricity i|- of an inch, will carry the point a to a\ and when the 



PLAIN SLIDE-VALVE, 21 

valve is in that position it must not overrun the edge of the 
bridge, but rather there must be width enough remaining to 
prevent leakage. The least width of bridge in the figure is f 
of an inch, and the width of \ inch is chosen to insure a joint. 

The forward-stroke inside lap, -f-^ of an inch, is laid off at 
cd. The greatest displacement of the valve will carry the point 
d to d\ and at that position of the valve the remnant of the 
exhaust-space should be at least as wide as the port, i.e. -^-^ of 
an inch as shown. The exhaust-space is commonly made wider 
than this construction gives ; it should not be unduly increased, 
since it will then make the valve large and the friction excessive. 

The valve is completed by making the width of the bridge 
\ of an inch and of the port, -f^ of an inch, as shown. If the 
eccentricity, \\ of an inch, be laid off toward the left, from the 
right-hand edges of the valve, it will appear that the right-hand 
bridge is wider than necessary, and that the remnant of the 
exhaust-space, when the valve has its maximum displacement 
to the left, is greater than the width of the steam-port. No 
inconvenience will occur from such an excess of bridge or 
exhaust-space ; but had the construction been begun at the 
right hand, then both the bridge and the exhaust-space would 
be too narrow. For constructive reasons, the bridge for any 
slide-valve maybe made wider than required to. prevent leakage. 

Fig. 3, PL V, gives the section (half-size) of a valve with 
equal laps which will give the same average cut-off as the valve 
shown by Fig. 2 ; the cut-off at the head end will be longer, 
and that at the crank end will be shorter. The outside lap for 
Fig. 3 is very nearly the mean of the unequal outside laps of 
Fig. 2 ; and the inside lap is very nearly the mean of the inside 
laps of the same figure. Such a valve may be laid off, begin- 
ning at either end. 

The height of the exhaust-cavity of the valve should never 
be less than the width of the steam-port ; it is commonly once 
and a half as high, if not more. 

The method just given for laying out the slide-valve has 



22 VALVE-GEARS FOR STEAM-ENGINES. 

the apparent inconvenience that the centre of the exhaust- 
space cannot be directly located on the assembly drawing of 
the engine. This difficulty is, however, only apparent, for the 
section of the valve is commonly drawn separately and at full 
size, and then can be transferred to the assembly drawing, 
which may be to any convenient scale. The results obtained 
by laying out the work on the drawing-board should always be 
checked by a numerical calculation ; and if desired such a 
numerical calculation may be made first, but it should be 
checked by the subsequent laying out of the valve. Thus the 
width of the bridge should be greater than 

^\ —\\ — tV = If' <^^ nearly | of an inch ; 
and the exhaust-space should have a width of 

tV + li + tV - ¥ = If of an inch. 

Equalization of Cut-ofT with Rocker. — A method of 
equalizing the cut-off without destroying the equality of the 
lead was devised by Professor Sweet, and is employed on the 
Straight Line engine. The same method may be employed 
with a bell-crank lever; the construction must, however, be 
carried out for each case separately. 

On Plate VI the centre-line of the crank and connecting- 
rod is xX' , while the centre-line of the valve-spindle is nn' , 
Assuming that the cut-off is to occur at f of the stroke, divide 
the diameter XX' of the crank-pin circle into fourths and draw 
the vertical line NR^ from N\ in the figure the eccentric-circle, 
drawn to a larger scale than the crank-circle, happens to pass 
through N. Make the angle XOR^ equal to the lead-angle, 
and bisect the angle RaOR^ by the line OP. Draw the valve- 
circle on (9Pand the lap-circle ^^', thus finding the outside lap. 

With C and C ,^\. f of the forward and return strokes as 
centres, and with the length of the connecting-rod as radius, 
intersect the crank-circle at R^ and i?/, to find the crank-posi- 



PLAIN SLIDE-VALVE. 2$ 

tions at cut-off. Produce the line R^O to RJ, the crank- 
position at admission for the return stroke. 

Since the gear is drawn with a rocker, the eccentric will 
follow the crank at an angle equal to XOP. The positions, r^ 
and r/, of the eccentric at cut-off will be found by laying off the 
angles Rfir, and RJOrJ, equal to XOP', and the positions of 
the eccentric, r^ and rj, at admission are found by making the 
angles RaOr^, and RJOrJ equal to the same angle. 

With r^ and r^ as centres, and with a radius equal to the 
length of the eccentric-rod, draw two arcs intersecting at e^ ; 
also with the same radius draw arcs from rj and rj intersecting 
at e] then if the end of the eccentric-rod be guided on a path 
passing through e and e^ the lead and cut-off will both be 
equalized. With a radius equal to the length of the arm of the 
rocker, 'draw arcs intersecting at T^ , and from T^ draw an arc 
through ee^ , and also the chord ee^ ; the length of the chord is 
greater than twice the lap ; consequently the other arm of the 
rocker should be made smaller than T^ey in proportion as the 
lap is less than half ee^ . The length of the other arm may be 
found by a numerical calculation, or by the following construc- 
tion: make ^^ equal to the lap, and draw st parallel to eT^\ 
then st is the required length of the rocker-arm. 

The construction may now be completed by shifting the 
centre of the rocker-shaft T^ , so that the other arm shall have 
the proper motion with regard to nn\ the centre-line of the 
valve-spindle. To make this construction, draw a line //' par- 
allel to nn', and at a distance equal to /^, taken from the triangle 
sqt or found by calculation from a proportion involving the 
side T^g of the triangle eT^g. With 6^ as a centre and with a 
radius equal to OT^ intersect the line //' at T; this gives 
the position of the centre of the rocker-shaft. With 7" as a 
centre the arcs da^d' and dc^d^, on which the ends of the rocker- 
arms travel, can be drawn. At the same time that T^ is swung 
to T, the point e„ is swung to c„ , found by intersecting the arc 
dd^ from O with a radius equal to Oe^ . From T draw Ta^ per- 



24 VALVE-GEARS FOR STEAM-ENGINES. 

pendicularto ;2;2'; then c^Ta^ is the position of the rocker when 
the valve is in mid-position, and aa' is equal to twice the lap. 
The position of the eccentric will be found by moving it 
through an angle equal to TOT^ \ and in the same direction ; 
thus when the crank is at ORd (the crank-end admission) the 
eccentric is at r/^ found by making rJOrJ'^= TOT^. The 
heavy black lines are drawn to show the eccentric, eccentric- 
rod, and rocker at the crank-end admission. 

The true position of the eccentric is of importance only in 
setting the valve and need not be known exactly even then. 
The extreme positions of the eccentric-rod and of the rocker 
are to be found by trial, and from them the extreme positions 
b and b' of the head of the valve-rod or valve-spindle. Since 
this method of equalizing the cut-off introduces some irregu- 
larity, a complete study of the valve-motion, by aid of the valve- 
ellipse or otherwise, is desirable. 

Piston-valve. — If the section of a plain slide-valve and its 
seat, as shown by Fig. 3, PI. I, be supposed to revolve about 
an axis xx'y there will be generated a piston-valve with its cy- 
lindrical seat. Such a valve is represented by Fig. i, PL VII, 
which gives a section of the high-pressure cylinder and valve 
of the U. S. battle-ship Massachusetts. It will be seen that the 
outside shell of the cylinder, the lower cylinder-head, and the 
valve-chest form one casting, with feet attached for bolting to 
the engine-frame. A cylinder-liner is forced into and secured 
to the outer shell, with a space between to serve as a steam- 
jacket. The piston is of conical form, and the heads are 
shaped to correspond. Leakage is prevented by two packing- 
rings held in place by a junk-ring. 

The piston-valve is in the shape of two pistons connected 
by a pipe or sleeve through which the valve-spindle passes. 
The valve-spindle is prolonged beyond the valve and attached 
to a small balancing piston which relieves the valve-gear of the 
weight of the valve and attached parts ; the upper end of the 
balancing cylinder is connected with the exhaust. The valve- 



PLAIN SLIDE-VALVE. 2 5 

seat is formed by two short hollow cylinders, forced into the 
shell of the valve-chest. The space surrounding each half of 
the valve-seat is connected with and forms part of the passage 
leading to the cylinder. The ports are cut through the cylin- 
drical valve-seat as shown. 

Steam is supplied to the middle of the steam-chest, and is 
exhausted from the ends through pipes shown by dotted circles. 
This arrangement secures the advantages that the supply and 
exhaust steam are kept well separated so that heat cannot 
easily pass from one to the other, and the valve-rod stuffing- 
box is exposed to the exhaust steam only ; such an arrange- 
ment is not advisable for a cylinder in which there may be a 
vacuum, since the leakage of air inward, past the stuffing-box, 
is more troublesome than the escape of steam. The laps con- 
trolling the admission and cut-off are by this arrangement 
placed inside ; while the laps controlling the exhaust and com- 
pression are outside. To avoid confusion, it is advisable to 
distinguish them as steam-lap and exhaust-lap ; the design of 
the valve-gear by the aid of valve-circles or otherwise may 
with this understanding be carried out as usual. It will be 
noticed that the top-end steam-lap is the larger; while the top 
end exhaust-lap is the smaller, and is here a negative lap or 
clearance. This arrangement is adopted to hasten the cut-off 
and compression on the down-stroke and delay them on the 
up-stroke, but is not carried far enough to produce complete 
equalization. The greater lead at the lower end helps to com- 
pensate for the shorter cut-off and the weight of the recipro- 
cating parts. 

Leakage past the valve is prevented by packing-rings, like 
those of the piston, which form the acting-edges of the valve, 
To prevent the valve-rings from springing into the ports, 
bridges are left as shown at A, 

Double-ported Valve. — It is frequently difficult or impos- 
sible to get sufficient width of port for engines having a large 
diameter and short stroke, if the common plain slide-valve is 



26 VALVE-GEARS FOR STEAM-ENGINES. 

to be used. Fig. 2, PI. VII, shows a device, known as a double- 
ported valve, used in marine engineering to overcome this dif- 
ficulty. Each passage leading to the cylinder has two ports, 
and two slide-valves, joined together and forming one casting, 
to control the flow of steam through those ports. The inner 
valve resembles the common slide-valve, except that there is a 
communication through the top between its exhaust-space e^ 
and the exhaust-space ^of the outer valve. The outer valve is 
elongated enough to leave a steam-space {a and a') to supply 
the inner valve ; a bridge between e and a separates the 
exhaust of the outer valve from the steam-space of the inner 
valve, and is continued to the opening through the top of the 
inner valve. Fig. 3 gives, at the left hand, a transverse section 
through the exhaust space e, and at the right, through the 
steam-space a. The space a is drawn down toward the middle 
of the valve as shown, so that the valve may be made compact 
while providing sufficient area for the flow of steam. 

Allen or Trick Valve. — Fig. 4, PI. VII, shows a valve 
which is so made that a double admission of steam takes place 
at and near cut-off and admission. It is used with the link- 
motion and other gears which give a variable cut-off with the 
slide-valve, and is intended to remedy the defects due to the 
slow motion imparted to the valve at those points when the 
cut-off occurs early in the stroke. 

Through the body of the valve there is a passage ss' , and 
the valve-seat is cut away so that the distance from the outer 
edge of the passage to the edge of the valve-seat is equal to 
the outside lap of the valve. If the valve is displaced toward 
the right by the amount of the outside lap, the edge c of the 
valve is brought to the edge of the port a, and at the same 
time the edge of the passage / is brought to the edge d of the 
valve-seat. Consequently there is a double admission of steam 
to the port a, one in the usual way past the edge c, and the 
other under the right-hand end of the valve, past the edge doi 
the valve-seat, and through the passage s's. As the valve opens 



PLAIN SLIDE-VALVE. 2^ 

wider, the passage ss' is liable to be shut off by traversing past 
the farther edge of the port a, but when that happens the 
supply past the edge c is abundant. Near cut-off the passage 
ss' is again opened at s and gives a double supply of steam till 
cut-off occurs by the simultaneous coincidence of c with the 
edge of the port a, and of d with the edge of the passage /. 

A modification of this form of valve, used on the Arming- 
ton and Sims engine, is shown by Fig. 2, PI. IX. The valve is 
a piston-valve, taking steam at the middle and exhausting at 
the ends, and differs from the valve shown by Fig. i, PI. VII, 
in that the stem connecting the two ends of the valve is hollow, 
and in that there is a passage from this interior channel through 
the valve-face. In the figure the valve is giving admission to 
the head end, and steam enters the cylinder directly from 5 
at a, and also from 5 at b, through the hollow stem and thence 
through the passage in the valve-face. 

Balanced Valves. — When the difference of pressure be- 
tween the steam and exhaust pipes is large, the force exerted 
to hold a plain slide-valve against its seat is very large, and the 
friction of the valve on its seat is excessive. This consumes a 
needless part of the work developed by the engine, throws a 
severe duty on the valve-gear, and makes it difficult to main- 
tain the acting-surfaces of the valve and its seat in good con- 
dition. Various methods of relieving valves from part or all 
of the steam-pressure on them have been devised, resulting in 
what are called balanced valves. 

The piston- valve (shown by Fig. i, PL VII) has no press- 
ure on it to hold it against its seat, and is consequently per- 
fectly balanced. It is very commonly used for the high-pressure 
and intermediate cylinders of triple-expansion marine engines, 
and on high-speed engines under the control of a shaft-gov- 
ernor. When well made, and provided with packing-rings, 
there is no more reason for leakage than exists with the piston 
of the engine. Small piston-valves are commonly made with- 
out packing-rings, and then depend on the fit in the valve-seat 



28 VALVE-GEARS FOR STEAM-ENGINES, 

to prevent leakage. It is claimed that they do not leak when 
new, that the wear is insignificant, and that both valve and 
seat may readily be renewed when necessary. It is, however, 
probable that such piston-valves do frequently leak in common 
service. 

The double-ported valve (Figs. 2 and 3, PL VII) and the 
Allen valve (Fig. 4, PI. VII) have part of the pressure on the 
back relieved, and are known as balanced valves. The double- 
ported valve has a shallow cylindrical recess turned in its back. 
In this is a short cylinder or ring that is pressed by springs 
against a finished surface on the valve-chest cover. A bronze 
ring fastened to the valve and bearing against the vertical 
ring or cylinder is intended to prevent leakage. Communica- 
tion is opened between the enclosed space and the exhaust, so 
that the leakage may not accumulate in this space and destroy 
the balancing of the valve. The unbalanced pressure of the 
steam on the unenclosed part of the valve gives enough press- 
ure against the seat to prevent leakage. The Allen valve is 
commonly much longer than wide, and consequently a rect- 
angular balancing-frame is used to exclude pressure from part 
of the top of the valve. Leakage into the enclosed space is 
allowed to flow directly into the exhaust-cavity through a 
small round passage, shown by dotted lines. All such devices 
are somewhat costly to make and troublesome to maintain in 
good condition, and if allowed to get out of condition are liable 
to a large loss from leakage directly into the exhaust. 

Valve-setting. — A slide-valve is commonly set to give equal 
lead, or else equal cut-off. Sometimes the leads are made un- 
equal, so as to partially equalize the cut-off ; in this case the 
jnethod of setting is like that used for equal lead, except that 
the lead at each end is made the amount determined on. If 
the cut-off is equalized by aid of a rocker or bell-crank lever, 
as shown on Plate VI, the valve is set to give equal lead. 

As a preliminary to the setting of the valve, a method will 
be given for putting the engine-crank on the dead-centre. 



PLAIN SLIDE-VALVE. 29 

To put an engine on the dead-centre. — In Fig. i, PI. VIII, 
let the circle C^CC^C be the path of the crank, and let A^A^ 
be the stroke of the cross-head ; while abed represents the edge 
of the fly-wheel or the face of the crank-disk, if the crank is so 
made. Set the engine with the cross-head near the middle of 
the stroke, and make reference-marks or take measurements 
so that it may be set again in the same position. Make a ref- 
erence-mark on the circle abed, and on some fixed object, at a 
and 0. Turn the engine round till the cross-head again comes 
to A ; the crank will then be at C\ and the mark made at a 
will be found at c. Make another mark at a, and bisect the 
arcs abc and adc at b and d. It is apparent that the angular 
distance of b from a is equal to the angular distance of C from 
C^ ; consequently the crank will be at the dead-point C^, if the 
mark at b is brought opposite 0. Also the crank will be at the 
dead-point C^ when d is brought opposite 0. 

In this process, and during all the operations of valve-set- 
ting, the engine and the valve-gear should always be moved in 
the direction in which the engine is intended to run, so that 
the lost motion or back-lash may be tal<:en up in the right way. 
Should the engine or the gear be moved too far at any time, 
then it should be turned back beyond the desired point, and 
brought up to that point with a motion in the right direction. 
Should the elasticity of the engine-belt interfere with the con- 
venient and accurate setting of the engine, it may often be 
possible to place a stick of timber under a fly-wheel arm, block 
up one end and place a jack-screw under the other, and so force 
the engine to the desired setting and hold it at will ; or some 
equivalent device may be used. 

To set a valve with equal lead. — First method. — Set the engine 
on a dead-point and give the eccentric the proper angular ad- 
vance, as near as may be ; making it too much rather than too 
little. Adjust the length of the eccentric-rod or of the valve- 
spindle to give the valve the proper lead. Move the engine 
forward to the other dead-point, and measure the lead ; if it is 



30 VALVE-GEARS FOR STEAM-ENGINES. 

not right, then correct half the error by changing the length 
of the valve-spindle, and the other half by moving the eccen- 
tric. Repeat till the result is satisfactory. 

If a valve-gear has a rocker, then the length of the valve- 
spindle should be such that the rocker may swing as designed ; 
usually to an equal angle on each side of a perpendicular 
through its axis, to the centre-line of the eccentric-rod motion. 
In such case the eccentric-rod only should be changed in 
setting the valve ; a small change of the valve-spindle may 
be allowed. 

Second method. — A valve that has harmonic motion will 
give the same maximum port-opening when set with equal 
lead. Such a valve may be set for equal lead by the following 
method. Valves which do not have harmonic motion cannot 
be so set ; as examples may be quoted a slide-valve having 
equal lead and with the cut-off equalized by aid of a rocker or 
bell-crank lever, and a valve controlled by a link-motion or 
radial valve-gear ; the two last forms will be described in future 
chapters : 

Loosen the eccentric on the shaft, and turn it around till it 
gives the maximum port-opening first at one end and then on 
the other. If the maximum port-openings are not equal, make 
them so by changing the length of the valve-spindle by half 
the difference; this operation adjusts the length of the valve- 
spindle. When that adjustment is complete, set the engine on 
a dead-point and give the valve the proper lead by turning the 
eccentric on the shaft ; this adjusts the angular advance. This 
method is convenient when it is difficult to turn the engine. 

To set a valve for equal cut-off. — With the crank on the 
head-end dead-point, give the eccentric the proper angular ad- 
vance, and give the valve the proper lead. Move the engine 
forward till cut-off occurs, and measure the displacement of the 
cross-head from the beginning of the stroke. Move the engine 
forward, again, till cut-off occurs on the return stroke, and 
measure the displacement of the cross-head from the crank end 



PLAIN SLIDE-VALVE. 3 1 

of the stroke. Should the cut-off be earHer at the head end 
than at the crank end, the valve-spindle is too long ; and con- 
versely it is too short if the crank-end or return-stroke cut- 
off is the earHer, In either case, change the length of the 
valve-spindle by an amount which it is estimated will correct 
the inequality ; it may be convenient to draw a valve-diagram 
to aid in making an estimate for a large engine. Set the 
engine again on the head-end dead-point, and adjust the lead 
by moving the eccentric. Try the cut-off again, and repeat 
till the result is satisfactory. 

It is apparent that a valve that is designed for equal cut-off 
Avill be properly set if the leads are made what the design gives 
for them. When such information is at hand, the process of 
setting the valve will be the same as the first method except 
that the lead at each end is to be made the proper amount, with 
the addition that the displacement of the cross-head is to be 
determined for each stroke, and the adjustment is to be com- 
pleted by the method just given. 

To set a valve with the steam-chest cover on. — Figs. 2 and 3, 
PI. VIII, show an arrangement by aid of which the valve may 
be set with the steam-chest cover on, and, if convenient, with 
steam applied to the engine. In preparation the valve is set 
to give the proper lead at each end, and a centre-punch mark 
IS made on the valve-spindle outside of the stuffing-box. A 
pair of trams are made of heavy wire, and adjusted so that 
they shall reach from the mark on the valve-spindle to a mark 
on the steam-chest, one at one dead-point and one at the other. 
In setting the engine, the first method for equal lead is to be 
used, with the difference that the valve is set to give the lead, 
when the engine is on a dead-point, by aid of the trams. A varia- 
tion of this method maybe used, for which one tram is required 
and two centre-punch marks are made on the valve-spindle. 
The method is convenient for locomotives, and it is customary 
to provide trams for this purpose in the tool-chest of the loco- 
motive, so that the valves may be set, if necessary, on the road. 



32 VALVE-GEARS FOR STEAM-ENGINES. 

It should be noted that the method of setting the valve 
with equal lead or equal cut-off insures that the action of the 
valve shall be what is desired when opening or closing. Any 
error of design due to the neglect of the angularity of the 
eccentric-rod is therefore transferred to some other part of the 
motion of the valve, namely, to a place where the valve is open 
or closed, and any irregularity of motion is then of little con- 
sequence. 



CHAPTER 11. 
ADJUSTABLE ECCENTRICS. 

Reversing with Loose Eccentric. — The device shown by 
Fig. 4, PI. VIII, was used for reversing some of the earliest 
locomotive and marine engines ; it is to-day used for reversing 
small and unimportant engines, and with some modifications 
to secure positive action, is used on engines of considerable 
power. As shown, the crank is at C, and the eccentric has its 
centre at E, so that the engine will run in right-handed rotation 
as shown by the arrow. The eccentric is loose on the shaft 
and has a pin at B, which engages with the end of a circular 
slot in a disk back of the eccentric, so that the eccentric is 
driven by the disk. To reverse the engine, it is stopped, and 
the eccentric or the engine is turned till the pin B engages 
with the other end of the slot at B\ 

The valve- circles for forward and for backward motion are 
drawn at OP and OP', and the lap-circle is nn^n^ ; the cut-off 
occurs at OR, on the forward stroke when running right-handed, 
and at 0R\ on the forward stroke when running reversed. 
The valve-circles for the return stroke are omitted to avoid 
confusion. 

Shifting Eccentric with Variable Lead. — A shifting 
eccentric, like that shown by Fig. i, PI. X, may be used for 
reversing an engine, and it possesses also the property of giving 
a variable cut-off. The eccentric is swung on a pivot S, a 
point on the centre-line of the eccentric and eccentric-rod 
motion, and is slotted to clear the shaft ; the angle OSO' is 
made equal to ESE', so that the centre of the eccentric may 
be brought to the point E' when the engine is reversed. Let 

33 



34 VALVE-GEARS FOR STEAM-ENGINES, 

the lap of the valve be equal to Ob ; then the displacement of 
the valve when the engine is on a dead-point is Oa^ found by 
drawing the vertical EaE' , and the lead is ba. 

In Fig. 2 the valve-circle OP represents the valve-motion 
when the eccentric-centre is at E. The cut-off occurs at the 
crank-position OR^ or at the piston-displacement xa, assuming 
harmonic motion ; with crank and connecting-rod the piston- 
displacement will be longer at the forward-stroke cut-off, and 
shorter at the return-stroke cut-off, but in such case xa is 
nearly the mean for the two strokes. When reversed the 
motion of the valve will be represented by the dotted valve- 
circle OP' . 

Suppose now that the eccentric-centre is shifted to E^ , Fig. 
I ; the angular advance is YOE^ , and the eccentricity is OE^, 
The valve-circle OP^ will represent the motion of the valve ; it 
has the angle YOP^ equal to the angular advance, and the 
diameter OP^ equal to the eccentricity when the eccentric- 
centre is at E^ , Fig. i. The point P^ is evidently on an arc of 
a circle having its centre on XOX^ produced, and drawn with 
a radius equal to ES, Fig. I. In like manner the valve-circles 
OP^ and OPq represent the motion given to the valve when 
the centre of the eccentric is at E^ and at E^, respectively. 
The piston-position at cut-off for the valve-circle OP^ is a^ ; 
the cut-off for the valve-circle OP^ is at a^ , and for the valve- 
circle OP^ is at a^. Thus it appears that the cut-off may be 
made to vary from the piston-displacement xa to the piston- 
displacement xa^ ; that is, from ^ to ^ oi the stroke. All the 
other events of the stroke, namely, compression, release and 
admission, vary at the same time as the cut-off, and in a simi- 
lar manner, though to a less degree. Of these other events, 
the admission varies the least ; an examination of the figure 
will show that the lead-angle increases from about 2° to about 
40°. The lead increases from ba to bE^ , Fig. i, and the increase 
is as clearly shown by Fig. 2. A circle representing the inside 
lap would, if drawn, show the change of release and compression ; 



ADJUSTABLE ECCENTRICS. 35 

it is omitted to avoid further complexity. Such a circle would 
show that the compression varies less than the cut-off, and 
that the release varies more than the admission. It is appar- 
ent that the increase of the lead depends on the radius SE 
(Fig. i) of the arc on which the eccentric-centre moves, and 
may be diminished by moving the pivot 5 away from the axis 
of the shaft. 

The gear is said to be in full-gear forward when the eccen- 
tric is at OE^ Fig. i, and at full-gear backing when the eccen- 
tric is at OE' , When the eccentric is at OE^ the gear is said 
to be at mid-gear; intermediate positions may be called grades. 
An examination of Fig. 2 will show that, since the centre of the 
valve-circle OP^, is on the axis XOX' , the crank-angle at admis- 
sion is equal to the crank-angle at cut-off, and this, with other 
considerations, will indicate that the mid-gear position of the 
eccentric does not give a proper motion of the valve for either 
forward or backing motion of the engine. 

Shaft-governor. — At the present time the shifting eccen- 
tric is widely used on high-speed engines, which have the valve 
under the control of a shaft-governor. Fig. i, PI. XI, shows the 
valve-gear of the Straight Line engine. The line XX' is the 
centre-line of the piston, crank and connecting-rod ; xx' is the 
line of the valve-spindle. The cut-off is equalized for one grade 
by aid of a rocker, and is not far from equal at other grades. 
The eccentric is pivoted at S, so that OS is the centre-line of 
the eccentric and eccentric-rod motion. The rocker oscillates 
on a centre at 2", and the arms Ta and 7"C are connected, respect- 
ively, with the valve-spindle xx' and the eccentric-rod CE, The 
governor consists of the weight Wand the spring LQ. The 
governor-lever WNM is pivoted at iV, and is connected by the 
link MVL to the eccentric casting at F, and to the five-leaved 
spring QL at L. When the engine is at rest the weight W 
lies against the fly-wheel boss as shown, and the eccentric is at 
full-gear. When the engine comes up to speed, the centrifugal 
force acting on W enables it to compress the spring QL, and 



36 VALVE-GEARS FOR STEAM-ENGINES. 

at the same time to move the eccentric toward mid-gear, and 
thus the governor adjusts the cut-off, and consequently the 
steam-supply, to the load. Since the engine is never reversed, 
the eccentric is slotted to clear the shaft only far enough to 
bring its centre to mid-gear. Fig. 2 shows the valve-diagrams 
for this gear drawn to an enlarged scale. 

In order that a shaft-governor may be able to control the 
valve of an engine, and maintain the speed nearly uniform, 
without being of excessive size, the valve must be nicely 
balanced and must move very freely. The Straight Line 
engine has a flat valve that moves between its seat and a 
cover-plate with enough clearance to avoid friction, but not 
enough to allow of leakage, just as a piston-valve moves in 
its cylindrical seat. A device similar in effect to the passage 
through the body of the Allen valve gives a double admission 
at and near cut-off and admission. The piston-valve, usually 
without packing-rings, is commonly used in connection with 
the fly-wheel governor. 

The action of the reciprocating parts of a high-speed engine 
is of great importance. A considerable part of the work of 
the steam is expended in imparting motion to the reciprocating 
parts during the first half of the stroke, and this stored energy 
is restored during the second half of the stroke as the recipro- 
cating parts come to rest. In order that they may come to 
rest quietly at the end of the stroke the piston should be 
cushioned by compression. Now a valve that gives a variable 
cut-off and a variable compression is likely to have too little 
compression at full-gear and too much at a short cut-off. An 
engine with a large clearance will suffer less from this difficulty 
than one with a small clearance ; consequently the clearance of 
high-speed engines with shaft-governors is often made large, 
but a large clearance is not conducive to economy in the use 
of steam. Now, lead acts, as does compression, to stop the 
reciprocating parts and to fill the cyHnder with steam, so that 
in general the more compression an engine has the less lead 



ADJUSTABLE ECCENTRICS. 37 

it will need. But it has just been seen that the shifting eccen- 
tric shown on Plate X has an increasing lead toward mid-gear, 
that is, at the time when it is least needed on a stationary 
engine. Had the pivot 5 been placed on the other side of 
the shaft, then the lead would have decreased toward mid- 
gear. Fig. I, PI. XII, gives the valve-diagrams for such an 
eccentric. Some forms of the Straight Line engine have their 
valve-gears so arranged in order that the decreasing lead 
toward mid-gear may partially compensate for the increasing 
compression. 

Shifting Eccentric with Constant Lead. — Fig. 2, PI. XII, 
shows an eccentric that has a motion square across the shaft, 
thus carrying the centre of the eccentric on the straight line 
EE^E' from full-gear forward to full-gear backing. It is at once 
apparent that the lead is constant. Fig. 3 gives the valve- 
diagrams for the full-gear, mid-gear, and two intermediate 
grades. Though the lead is constant, the lead-angle is not so ; 
a comparison with Fig. 2, PL X, will show that the variation 
is not so much as that of the lead-angle for an eccentric with 
increasing lead, but it is more than for an eccentric with de- 
creasing lead, as may be seen by a comparison with Fig. i, 
PL XII. 

A shifting eccentric with constant lead must be slotted to 
clear the shaft ; the line 00' is made equal to EE\ in order 
that E may pass to EE' when the engine is reversed. If the 
engine runs always in one direction, the slot, from centre to 
centre, may be only as long as EE^. 

The shaft-governor of the Armington and Sims engine, 
shown by Fig. i, PL IX, is equivalent to a shifting eccentric 
with constant lead. The eccentric ^ is on a casting, ab, loose 
on the shaft ; the eccentric E^ is loose on the eccentric E. The 
weights W and V compress the springs N and My and move 
out toward the rim of the wheel as the engine comes up to 
speed. The links ac and bd take hold of the eccentric-casting 
ab^ and the link st takes hold of the eccentric ^,. As the 



38 VALVE-GEARS FOR STEAM-ENGINES. 

weights move out the linkage cabd takes a new position, such 
as ^V^'^', turning the eccentric E toward the left; at the 
same time the link st takes the position s'f^ turning the eccen- 
tric E^ toward the right. The proportions of the mechanism 
are so chosen that the centre, e, of the outer eccentric, E^y 
moves straight across the shaft to a new position, e', and the 
cut-off is shortened. It will be seen that the effect is the same 
as that of the shaft-governor of the Straight Line engine, ex- 
cept that the lead is constant. 



CHAPTER III. 
LINK-MOTION. 

The valves of locomotives, marine engines, and other re- 
versing engines are commonly controlled by a mechanism 
called a link-motion ; this mechanism has also the property 
of giving a variable cut-off. The mechanism consists essen- 
tially of two eccentrics, one for full-gear forward and one for 
full-gear backing, together with the eccentric-rods and the 
link. The eccentric-rods are attached to the link, at or near 
the ends, and the link is slotted or otherwise arranged to 
receive a block on the end of the valve-spindle, on a radius- 
rod, or the end of a rocker, as the case may be. The link- 
motion takes two forms ; in one, known as the Stephenson or 
shifting link, the link is moved on the block to reverse the 
engine or vary the cut-off ; in the other, known as the Gooch 
or stationary link, the block is moved in the link to accompHsh 
the same object. 

Stephenson Link. — The usual form of Hnk-motion for 
American locomotives is shown by Figs, i and 2, PI. XIII. 
The valve is moved through a rocker so that the eccentrics 
follow the crank ; thus, the centre of the crank is at C, and the 
go-ahead eccentric has its centre at E, while the backing ec- 
centric centre is at E' , The link-pins P and P' , to which the 
eccentric-rods are attached, are set back from the link-arc, and 
the link may move over the link-block B so far as to bring the 
centre of the block opposite the centre of the link-pin, as 
shown by Fig. i ; in which position the motion of the valve is 

39 



40 VALVE-GEARS FOR STEAM-ENGINES. 

controlled almost entirely by the eccentric E, and has essen- 
tially the motion of a plain slide-valve. The link is suspended 
by a link or hanger, nm^^ from a reverse-shaft centred at S; the 
hanger takes hold of the saddle-pin m^ on a plate that is com- 
monly at the middle of the link. 

A locomotive has two cylinders, with pistons acting on two 
cranks set at a right angle, and thus has two engines each of 
which must be provided with its own link-motion. Both links 
are suspended from one reverse-shaft, which has an arm SR 
from which a rod runs to a reverse-lever conveniently located 
in the engineer's cab. The reverse-lever moves over a notched 
arc, and by aid of a latch engaging with the notches the link 
may be set and secured in any desired position. 

Fig. 2, PI. XIII, gives an end elevation of the link, the 
hanger, and one arm of the rocker carrying the link-block B. 

English locomotives commonly have the link act directly 
on the valve-spindle, without the intervention of a rocker. In 
such case the link-pins should be placed on the link-arc, as 
shown by Fig. 3, PI. XIII, and consequently the link-block 
cannot be opposite one of the link-pins and cannot receive the 
full motion of the eccentric. Consequently the eccentricity, 
and with it all the dimensions of the link-motion, must be 
larger to give proper motion to the valve. 

The link-motion for the high-pressure cylinder of one of 
the engines of the U. S. S. Maine is shown by the figures on 
Plate XIV. The parts are lettered as on Plate XIII ; thus E 
and E' are the centres of the eccentrics, and P and P' are the 
link-pins, which in this case are on the link-arc ; vS is the reverse- 
shaft, and iVPis the drag-link or bridle which takes hold of the 
go-ahead link-pin. The link, which is known as the Scotch or 
side-bar link, is shown in plan by Fig. 2. The link-block is 
between the side-bars, and is pivoted directly on the end of the 
valve-spindle ; thus the link can be set so that the axis of the 
link-pin coincides with that of the link-block pivot, and the 
full motion of the eccentric can be given to the valve. The 



LINK- MO TION. 4 1 

head of the valve-spindle is guided by cast-iron jaws, as shown 
in Fig. I. The end of the reverse-arm is slotted and provided 
with a sHding-block, screw, and hand-wheel as shown, so that 
the cut-off may be adjusted in a manner to be described later. 
Open Rods and Crossed Rods. — If the eccentric-rods of a 
link-motion are connected as shown in Fig. i, PL XV, the 
rods are said to be open ; on the other hand, the rods are said 
to be crossed when connected as shown by Fig. 2. In both 
figures the crank is on the crank-end dead-point, and the valve- 
gear has no rocker. A link-motion with a rocker is said to 
have open rods when the eccentric-rods are connected as shown 
by Fig. 3; aTb is the rocker, and be the valve-spindle-, the 
crank is on the head-end dead-point. In all these figures the 
link-pins are on the link-arc. Since half a revolution will 
apparently cross the rods for Figs, i and 3, while it will appar- 
ently open the rods for Fig. 2, the nomenclature seems to be 
unfortunate. There is, however, a real difference in the methods 
of the connection of the rods, and that difference has an im- 
portant influence on the action of the valve, for open rods give 
an increasing lead from full toward mid gear, while crossed 
rods give a decreasing lead from full toward mid gear. In Fig. 
I, the full lines Ep^, E'pJ, and the arc/^^/, show the eccentric- 
rods and the arc of the link at mid-gear, while the thin lines 
Ec, E'p' , and the arc cp' , show them at full-gear forward. Since 
the valve and valve-rod have the same motion as the link-block, 
it will be sufficient to trace the motion of the latter. At full- 
gear the link-block will be at c^ found by intersecting the line of 
centres with ^ as a centre, and with a radius equal to the 
length of the eccentric-rod. The eccentric-pin p' is located by 
drawing arcs from E' and c, with the lengths of the eccentric- 
rod and the length of the link as radii. At mid-gear the link- 
block is ac^\ the points p^ and // are at a distance from the 
centre-line OX^ equal to half the chord of the link-arc, and the 
link is erect. The increase of lead from full-gear to mid-gear 
is apparent from the diagram. A similar construction in Fig. 



42 VALVE-GEARS FOR STEAM-ENGINES. 

2 shows the decrease of lead from full-gear toward mid-gear for 
crossed rods. In the figure the decrease is greater than the 
full-gear lead, so that the valve is shut at the dead-point when 
the link is at mid-gear. 

Long and Short Rods. — The variation of lead from full- 
gear toward mid-gear is due to the curvature of the link-arc, 
and is more pronounced for a link with short radius than for one 
with long radius ; now the radius of the link-arc is usually equal 
to the length of the eccentric-rod, hence the variation is more for 
short than for long rods. In Fig. i, PI. XV, it is apparent that 
c"c^' is greater than cc^ ; a similar construction will show that 
the decrease of the lead from full-gear to mid-gear for crossed 
rods is more marked for short than for long rods. 

Radius of the Link-arc. — An analytical discHssion of the 
link-motion shows that the radius of the link-arc should be equal 
to the length of the eccentric-rod ; if the link-pins are on the 
link-arc, then the radius should be the distance from the centre 
of the eccentric to the link-pin ; but if the pins are back of the 
arc, the radius is the distance from the centre of the eccentric 
to the link-arc, i.e. the length of the rod plus the distance the 
pins are back of the arc. The same discussion establishes also 
the fact that open rods give increasing lead, and that crossed 
rods give decreasing lead, from full-gear toward mid-gear ; but 
the demonstrations given are believed to be useful, and a 
similar demonstration will be given of the proper radius for the 
arc. 

In Fig. I, PI. XV, the link-block is at c at full-gear when 
the crank is on the crank-end dead-point ; when the crank is 
on the head-end dead-point a similar construction will give 
for the position of the link-block the point c' , The point Oy 
half way between c and c' ^ corresponds to the mid-position of 
the valve, and from o the lap on^ on' may be laid off on each 
side, giving nc = n'c' for the lead. At mid-gear the head-end 
lead is nc^ , and a similar construction for the head-end dead- 
point will give n'c^ = nc^ for the head-end mid-gear lead. If 



LINK-MOTION. 43 

now a diagram is drawn for some intermediate gear of the link, 
it will be found that the lead is the same at the two ends, and 
that it is intermediate between nc and nc^. Fig. i is drawn with 
the radius of the link-arc equal to the length of the eccentric- 
rod, and any diagram drawn with dimensions chosen at random 
will in Hke manner show equal leads under like conditions. 
Constructions for a link with crossed rods will also show equal 
leads if the radius of the Hnk-arc is equal to the length of the 
eccentric-rod. Consequently it may be inferred that the one 
requirement for equal leads is that given, i.e., that the radius 
of the link-arc shall be equal to the length of the eccentric- 
rods. A natural inference is that any other radius for the link- 
arc will give unequal leads for some grades of the link, and 
such will be found to be the case if constructions are made. 

Analytical Discussion. — The best idea of the nature of 
the motion given by a link to the valve is obtained from an 
analytical discussion due to Zeuner, taken, with slight variations, 
from his Treatise on Valve-gears. 

On Plate XVI the Figures i and 2 are drawn to represent 
link-motions with open and with crossed rods. The diagrams 
in thin lines give the positions of the parts when the crank is 
on the crank-end dead-point ; and the diagrams in heavy lines 
show the positions when the crank has moved through the 
angle d. 

The eccentricity for each eccentric is r^ and the angular 
advance is S. The link-pins are on the link-arc, the length of 
the eccentric-rods is /, and the radius of the link-arc is p which 
may or may not be equal to /. The length of half the link-arc 
is Cy and the displacement of the link-block from the middle of 
the link-arc is d. In the discussion it is assumed that the link 
is supported and guided by the link-block so that the point n 
remains on the line XX' . It is also assumed that the chord 
joining the link-pins is equal to the length of the link-arc 
between those pins, and that in like manner the displacement 
of the link-block from the middle of the link may be measured 



44 VALVE-GEARS FOR STEAM-ENGINES. 

indifferently either on the link-arc or on the chord. The error 
of this assumption may be estimated as follows : A common 
proportion is r = J^ = y^^/, or ^ = |^/, so that the arc subtends 
an angle of about lo°, and for that angle the arc is 0.1745 of 
the radius and the chord is 0.1736 of the radius, and the error 
is a little more than half of one per cent. 

The distance from the centre of the driver-axle to the 
middle of the valve, in either Fig. i or Fig. 2, PI. XVI, is 



Ob = Om -{- mn ■\- nb ^^ Op — mp -f- mn -\- nb, , (7) 

in which the length of the valve-spindle iib may be replaced by 
Sy and the value of the other terms may be conveniently deter- 
mined as follows : 

First, the term mp is determined by the equation 

mp = mP sin mPp = (c — d) sin a, , » , (8) 
Now 

pp' Op - Op' 
sm« = ^, = ' ^9> 

Prom Fig. i, PI. XVI, 

Op=Oe^epz:^Oe-V'(EP' '-(Pp'-'Eef\''\ . (10) 
and from Fig. 2, 



0p=.0e^ep=0e^ \EP - (/> + Eey\\ . (il) 



LINK-MOTION. 45 

In either figure 

Oe = r sin {S -\-d\ Ee — r cos (B -\- d), EP = /, 
and 

Pp =z mP cos mPp ^^{c — d) cos a ; 

these values substituted in equations (10) and (11) give 

Op = rs\n{e-\-d)-[- {P — \{c — a)cosa ^ r cos(e-{-d)J\i', {12) 

the upper sign being taken for open and the lower sign for 
crossed rods. Expanding the term with a fractional exponent 
by the binomial theorem, and rearranging terms with the 
higher powers of / in the denominator, gives 



(c — dY cos' a 
Op = rsm{e + S)-\-l-^ ^^ 

(^ _ d)r co s {6 + S) co s a r" cos ' {B + d) 
± 1 H Yl 



Now the terms containing cos a in the numerator have / in 
the denominator, and are small compared with r sin {6 + 6\ 
while a is not more than 30°, for which the cosine is 0.866 ; 
consequently we may replace unity for cos a without much 
error. With that change and some expansion, 

c' cd d^ 
op = r sm(e^ 6) + I --^^-j--^ 

(c -d)r cos {O + S) r" cos' {S + 0) 



46 VALVE-GEARS FOR STEAM-ENGINES. 

Similarly Fig. i and Fig. 2 give respectively equations (14) 
and (15): 



Op' = e'p' - Oe' = \E'P' - {Ff - E'eJY - Oe' ; (14) 
Op' = // - Oe' = \E^" - {P'p' + E'e'y\^ - Oe\ (15) 

In either figure 

0/ = r sin {6 - 6), E'e' = r cos (B - S\ E'F = /, 
and 

P'p' = mP' cos mP'p' z=z{c-\- d^ cos a ; 

these terms substituted in equations (14) and (15) give 

(9/= -rsin(^ - ^)+ {/'-[(^+^) cos a':^r cos(^-d)]'}* ; (16) 

the upper sign being taken for open and the lower for crossed 
rods. As in the previous work, the cos a may be replaced by 
unity ; expanding by the binomial theorem, and rejecting terms? 
with the higher powers of / in the denominator, gives 



Op' = ^r sin (B.-d) J^l- ^'^J^' 

{c + d)r cos {B — 6) r" cos' {6 — S) 
^ 7 Yl 



^/="--(^-^)+^-S-?-S 



(c + d)r cos (6' - S) _ r" cos" (B ^ S) 



LINK-MOTION. 47 

Substituting in equation (9) the values for Op and Op\ 

r sin id -\-&)-^r sin {S — d) 2cd 
sma = + ^ 

(c -d)r cos {d-\-6)-{c-{- d)r cos (^ — 6) 
^ 2cl 

r' cos" {d-\-d)- r' cos' ( 6- d) 



T T dt 

.'. sin a = — cos (^ sin ^ =F -7 sin (5^ sin <9 ip -- cos S cos ^ 

+ 7 - ^/cos" (« + d) - cos' (^ - d)]. (18) 

To find the value of the term mn^ which in Fig. 3, PL XVI, 
is seen to be nearly equal to mj,^ we have 



mn = m^i = m^n^ — tn^ ; 



Pm, m c ^ / 1 X f . 

/. mn = — Tf. — T^ = (nearly). . (10) 

Substituting in equation (7) the values of the several terms, 

c' cd d" 
Ob = r sin S cos 6 -\- r cos ^ sin 6 -\- 1 J ~\~~T j 

K^-^). a ^ ' n ■ ^x ^'C0s'(d+^) 

± -^ — -^cos ^ COS ^ — sm sm d) /^ 

if T dv 

— COS S sin ^ =F y sin d sin ^ =F — 7 cos d cos 6^ 

+ / - ^/ 1"°'' (^ + <^) - <^°^" (^ - <^)3 } 

+ — - — + ^; 



48 , VALVE-GEARS FOR STEAM-ENGINES. 

Ob = r[s'm d ± — i — cos ^ ± (^ — d)—^ cos d] cos fi 

c — d , - c — d ^ c — d . «-,.„ 
-Y ^Lcos o =F — ^^ — sin o cos o ± — - — sin o] sin u 

- -^ I 2^ cos^ (p^-Q)-{c- d) [cos'((9 + <^) - cos' (O-d)-] I 
— ^'p -|- 2cdf> — d*f> — 2(<; — d)dp + ^'^ — <^V 

+ Wp + ^+^; 

/ c" —d" \ d 

,\ Ob = Asm d ± — cos dlcos -\- r— cos S sin 6 

- ^jiif + d) COS' {S + e) + {c-d) cos' (^ - <y)j 

+ ^^ - d')-ilf + I + s (20) 



The third term has its greatest value when d is equal to Cy. 
and it is then equal to 

y-' cos" {6 + d) 

2/ 



which is the term that appears in equation (5) for the plain 
slide-valvCa In the discussion of the plain slide-valve this term 
was neglected, and consequently it may be neglected here with 
equal propriety. Equation (20) may therefore be written 



Ob 



= r(sin 6 ± -J — cos d\ cos d -\-r— cos d sin 6 



-\-i^-^')-^ + l+'- ■ (2I> 



LINK-MOTION. 49 

If the engine is on the crank-end dead-point, then B is zero ; 
and it is 180° at the head-end dead-point. The special values 
of the crank-angle give 



Ob' = r[sm S ± --^j- cos d) + {/ - d'')-^ + /+ ^ ; (22) 
Ob" = - r[sm d ± ^--^ cos c^) + {c^ - ^)^ + l+s. (23^ 



The mid-position of the valve should be midway between 
b' and b", Figs, i and 2, PL XVI ; half the sum of Ob' and 
Ob'' is 



*=^^^ = (--^/-ir"+'+>. . ,,) 



in which the only variable is the term containing p, the radius 
of curvature of the link-arc. If p be made equal to /, then this 
term disappears, leaving 



Oo = /+s (25) 

Wttk equal laps^ the necessary and sufficient condition for 
equal leads, at all grades, is that the radius of the link-arc shall 
be equal to the length of the eccentric-rod. 

Applying this condition to equation (21) gives 

/ c^ — d^ \ d 

Ob = r( sin d ± ^ — cos djcos B -\-r— cos d' sin B -\- 1-\- s, (26) 



50 VALVE-GEARS FOR STEAM-ENGINES. 

The displacement of the valve from mid-position is 

e=Ob— Oo\ 
,\ e = z*! sin S ± — cos 8\ cos 6 -{- r— cos 8 sin Q. (27) 

General Equation for Valve-motion. — The equation (6) 
gives for the displacement of a plain slide-valve moved by an 
eccentric, 

e •= r sin {p -\- ^'i 

expanding the parenthesis, 

e =L r cos d sin 6 -\' r sin 6 cos 6^ ; , , , (28) 

which may be written 

e = A cos 6 -\- B sin 6, (29) 

since r and S are constant for a given slide-valve gear. 

It has been shown by the aid of Fig. 7, PI. II, that the 
motion of a plain slide-valve may be represented by a valve- 
circle, and a comparison of that figure with the equation (29) 
will show that the constants in the equation are the coordi- 
nates of the end P of the diameter of the valve-circle. Thus 

Og = rsind = A; (31) 

Pq z=r cos d = B , (32) 



LINK-MO TION. 5 1 

It may be concluded that any valve which has its displace- 
ment represented by an equation of the same form as equation 
(29) has a harmonic motion and may have its motion repre- 
sented by a valve-circle. 

Zeuner's Diagram. — A comparison of equation (27) with 
equation (29) shows that a valve controlled by a Stephenson 
hnk-motion has a harmonic motion, and that its displacements 
from mid-position, at any grade of the link, may be represented 
by a valve-circle, having for the coordinates of the end of the 
diameter 

A = r\sm ± ——^ — cos ^j ; .... (33) 

^ = r-cos6' (34) 

At full-gear d =^ c, which applied to equations (33) and (34) 
will reduce them to equations (31) and (32). Thus the valve- 
diagram for a link-motion at full gear is identical with the dia- 
gram for a plain slide-valve under the control of an eccentric 
having the same eccentricity and angular advance as one of 
the eccentrics of the link-motion ; which coincides with our 
conceptions of the link-motion, derived from the drawings on 
Plates XIII and XIV. 

In Fig. 4, PI. XVI, and Fig. i, PI. XVII, Oq and ^Pare made 
equal to the coordinates of the end of the valve-circle diameter 
at full-gear, when d=^ c\ i.e., 

Og = r sinS = Af qP = r cos d =1 B, 

At mid-gear d becomes zero, and the coordinates the end of 
the diameter of the valve-circle become 

A^=irsmd ±jC0s6\ (35) 

^0 = (36) 



52 VALVE-GEARS FOR STEAM-ENGINES. 

The upper sign is taken for open rods, and the lower sign for 
crossed rods. Fig. 4, Pi. XVI, corresponds with the first case, 
and Fig. i, PI. XVII, with the second case. The ends of the 
diameter of valve-circles for intermediate grades of the link 
may be found by assuming values for d and calculating the co- 
ordinates by aid of equations (33) and (34), if desired ; but an 
inspection of those equations shows that they give the co- 
ordinates of a parabola having its vertex on the axis XX\ 
Two points, P and P^^ are already located and an arc of the 
parabola may be passed through them by the ordinary geo- 
metrical construction ; or, since the arc is quite fiat, there may 
be substituted for it the arc of a circle having its centre on the 
axis XX' . The centres of the valve-circles have for their co- 
ordinates, \A and \B, and consequently lie on another para- 
bola with its vertex on XX' ; an arc of a circle centred on 
XX' may be substituted for the arc of the parabola, and will 
be more convenient to draw since its radius is half the radius 
of the circular arc substituted for the parabola through P and 

P.- 

Fig. 4, PL XVI, and Fig. i, PL XVII, exhibit the variation 
of lead which was pointed out in Figs, i and 2, PL XV. The 
same thing is evident from an inspection of equation (33), 
taking the upper sign for open and the lower sign for crossed 
rods. For convenience the fact is stated as follows : 

A Stephenson link-motion with open rods gives increasing lead 
from full-gear toward mid-gear ; with crossed rods it gives de- 
creasing lead from full-gear toward mid- gear. 

Valve-circles showing the motion of the valve at inter- 
mediate grades of the link are drawn at OP^ and OP^ , on Fig. 
4, PL XVI, and on Fig. i, PL XVII. On both figures the lap- 
circles are nn'n" y showing cut-off at the crank-positions ORy 
ORy^ , ORf y and OR^ ; neglecting the influence of the connect- 
ing-rod, the corresponding piston-displacements are xa, xa^ , 
xa^ y and xa^ . An inspection of the figure will show that the 



LINK-MOTION, 53 

lead-angle increases as the cut-off is shortened, accompanied 
by an earlier admission. If an inside lap-circle were drawn, it 
would show that an early cut-off is accompanied by an early 
release and a large compression. A comparison of these dia- 
grams with the valve-diagrams shown by Fig. 2, PI. X, and 
Fig. I, PI. XII, will show that a Stephenson link-motion is 
equivalent to a shifting eccentric with variable lead. 

Gooch Link. — Fig. i, PL XVIII, shows the Gooch or sta- 
tionary link, as applied to locomotive engines. E and E' are 
the forward and backing eccentrics, from which the eccentric 
rods lead to the link-pins P and P' , The link is suspended by 
the link mUy from a fixed pivot n^ and has its convex side 
turned toward the axle O. The link-block B is carried by a 
radius-rod BD, which is connected directly to the head of the 
valve-spindle at D, By means of a reverse-arm ST and hanger 
TU, the engineer may place the link-block B opposite the link- 
pin P for full-gear forward, opposite the link-pin P' for full- 
gear backing, or at any intermediate position. The action of 
this link-motion is therefore equivalent to that of the Stephen- 
son link-motion. The details of the mechanism are varied 
somewhat by different makers. In the figure the link is sus- 
pended from a saddle-pin on or near the chord joining the 
ends of the link-arc ; and for this purpose a plate or bridge 
similar to that shown by Fig. 2, PL XIII, is employed which 
permits the passage of the link-block. The saddle-pin is some- 
times placed behind the link-arc toward O, so as to avoid the 
use of a plate or bridge. The link-pins are placed behind 
the link-arc to allow the link-block to be brought opposite 
the link-pins. They may be placed on the link-arc, using a 
link like that shown by Fig. 3, PL XIII, but turned so that the 
convex side is toward the axle O ; in which case the full action 
of the eccentric cannot be given to the valve. Sometimes a 
box-link, shown by Fig. 3, PL XVIII, is used, and then the 
saddle-pin and link-pins may be placed in any desired positions 



54 VALVE-GEARS FOR STEAM-ENGINES. 

without interfering with the Hnk-block ; this device is equiva- 
lent to the side-bar link shown on Plate XIV. 

Open and Crossed Rods. — As was found to be the case 
with the Stephenson link, the rods of the Gooch link may be 
open or crossed. Fig. i, PL XVIII, has open rods, and Fig. 2, 
PL XVII, has crossed rods. 

Radius of the Link-arc. — The common and proper prac- 
tice is to make the radius of the link-arc equal to the length of 
the radius-rod ; and when so made the lead is constant for all 
grades of the link. This property is at once evident from in- 
spection of Fig. I, PL XVIII, and Fig. 2, PL XVII, one having 
open and the other crossed rods ; for it will be seen that when 
the engine is at a dead-point and the link is erect, the link- 
block may be moved from one end of the link-arc to the other 
without moving the valve. 

Analytical Discussion. — Making use of the same notation 
as in the analytical discussion of the Stephenson link, let e be 
the eccentricity, and S the angular advance for each eccentric ; 
let c be the half-length of the link, and d the displacement of 
the link-block from the middle of the link ; let / be the length 
of the eccentric-rod, the link-pins being assumed to be on the 
link-arc ; let /, be the length of the radius-rod, and s the length 
of the valve-spindle. 

Assume that the link is so suspended that m, the middle 
point of the chord, shall remain on the central line XX' y and 
that the length of the link is sensibly the same whether meas- 
ured on the chord or on the arc. Assume also that the rods 
are open. 

In Fig. 2, PL XVIII, the diagram in fine lines represents 
the link-motion when the crank is on a dead-point ; and the 
diagram in heavy line, represents it when the crank has 
moved iYOvaC^ to (7 through the angle 6, 

The distance from the origin to the middle of the valve b 
is 

Ob = Op-pk^kq-\-qS-^Sb (37) 



LINK-MOTION. 55 

The term//^ is determined by the equation 

pk = KP sin pPK ={c — a) sin or. (38) 

Now 

pp' Op - O p' . . 

sin or = -^ = (39) 

But 

Op =^ Oe -{-ep = Oe -^\EP ~(Pp-Eey\\', . (40) 



Op' =-0e'-\- e'p' = - 0/ + {£'r - {Py - Eey\K (41) 

in which 

EP=E'F=l, Pp = Pp' = ccosa; 

Oe = r sin {d + d), Oe' = r sin {0 — S)\ 

Ee = r cos (^ + S\ Ee' = r cos {0 - ^). 

Substituting these values in equations (40) and (41) gives 

Op = r sin (d -\^ d)-\-\P -\c zo^a - r cos {6 + S)-\'\\ ; (42) 

Op' z=-r sin (6> - d) +|/» _ [c cos or - ^-cos (^ - d)]''}i (43) 

A comparison of equations (42) and (43) with equations (12) 
and (16) shows that they differ in that the coefficient of cos a 
does not contain d, and that only the upper sign of the double 



$6 VALVE-GEARS FOR STEAM-ENGINES. 

sign appears before the last term in the bracket ; this last be- 
cause the discussion applies only to open rods. Consequently 
the value of sin a may be obtained from equation (i8) by omit- 
ting terms containing dy and using only the upper sign of 
the double signs ; hence 



r r 

sin or = — cos S sm 6 — -j sin S sin 6 
c I 

-^^[cos'(^+<y)-cos'(e-<y)]. (44) 



Expanding the term in equation (42) which has a fractional 
exponent, by the binomial theorem, and rejecting terms with 
higher powers of / in the denominator, and at the same time 
substituting unity for cos «r, will give 



0/ = rsin(e+<S) + /- g+^cos (^+<5)-^^^^?l^. (45) 



The first two terms of the equation (37) are now deter- 
mined ; the others are 

Sb = Sy 



^5 = 1/,'-^'}^=/, - — (nearly), 



2/, 



and 



' d' 



^^ = ji:-^ ^"^^'^>')- 



LINK-MOTION. 57 

To obtain the last equation, it may be admitted that qk 
(Fig. 2, PL XVIII) is nearly equal to QK^ which is nearly 
equal to tm. Now Pm is half of a chord bisected by a diam- 
eter, of which one segment is nm and the other is 2/^ — mn ; 
consequently 

Pn^ = nm{2l^ — mn) ; 
/. mn = -J- (nearly) ; 



and in like manner 



nt = —7- (nearly). 



/, tm= kq = -j J (nearly). 

Substituting the values of the several terms in equation (37), 

if f 

— sin 6^ cos d — y sin 6^ sin d 

+ ^^[cos'(^_^)^cos^(^+<y)]| 

"■27;'+2^+^^~2^+'^' 



58 VALVE-GEARS FOR STEAM-ENGINES, 



CT 

,% Ob=^r sin 6 cos 6 -^-r cos ^ sin ^ + -r cos 6 cos S 



CT CT 

J sin ^ sin (J — r sin B cos d -|- -^ sin ^ sin S 



dT „ </r , c^ c^ 
-|- — sin u cos (J — --^ sin 6' sin (J -[" ^ > ~ ~7~ + ^i + -^ 



- J^cos' (^ + <y) - ^^cos« (^ - tf) + J^ cos' (<; + tf) 



+0'=-'(^-<^)-s<=-x^+<^>' 



(^^ zz= r( sin <^ + -T cos Sj cos ^ -| 1 cos ^ -- y- sin <J Jsin 6 



3 a 

C C 



+ /+/. + . -^,-^ 



- ^/ K^ + '^^ ^°^'' (^ + <^) + (^ - '^) cos' (^ - '^)]- (46) 



The last term is identical with the term dropped from equa- 
tion (20), and it may be neglected here as well. 

At the crank-end dead-point 6 is zero, and it is 180° at the 
head-end dead-point. The corresponding values for Ob are 



(?/J' = r(sin<y + ^cos<y)+/ + /.+^-|J-^; {47) 



LINK-MOTION. 59 

^^-=_^(sind+|cos(^) + / + /,+5-|^-|,. (48) 

Hence the distance from the origin O to the middle of the 
valve, when in mid-position, is (Fig. 2, PL XVIII) 



Oo = \(pK-YOb:)^l-\-l,-^rs-'--'--^, . (49) 



The displacement of the valve from mid-position at any 
crank-angle is obtained by subtracting equation (49) from 
equation (46), member from member, giving 

e z=z rUm ^ -{-j cos (^ jcos -\ (cos (J — — sin djsin 6 . (50) 



Thus far in this discussion attention has been given to the 
case of open rods only ; were the same method to be carried 
through for crossed rods, using a figure similar to Fig. 2, PI. 
XVIII, a similar equation would be found for the valve-dis- 
placement, except that the quantities c and d would be affected 
by a negative sign. 

Zeuner's Diagram. — A comparison of equation (50) with 
equation (29) shows that a valve controlled by a Gooch link- 
motion has a harmonic motion, and that its displacement from 
mid-position, at any grade of the link, may be represented by 
a valve-circle. Taking account of the observation at the end 
of the previous paragraph, with regard to crossed rods, the 
co-ordinates of the end of the diameter of the valve-circle may 
be written 

A = r\s\n6 ±jCosSy^ (51) 



60 VALVE-GEARS FOR STEAM-ENGINES. 

B— — f cos d q= - sin (Jj ; .... (52) 



the upper sign being used with open and the lower with 
crossed rods. 

The expression for A, the abscissa of the end of the diam- 
eter of the valve-circle, is the same for all grades of the link; 
which agrees with the statement on page 54, that the lead is 
constant when the radius of the link-arc is equal to the length 
of the radius-rod. It is apparent, therefore, that a Gooch link- 
motion is equivalent to a shifting eccentric with constant lead. 
Fig. 3, PI. XVII, gives the valve-circles for full-gear, mid-gear, 
and for two intermediate gears ; and shows the variation of 
cut-off from full-gear to mid-gear. As was found to be the 
case with the shifting eccentric, constant lead is found to be 
accompanied by an earlier admission from full-gear toward 
mid-gear, though the change is not so marked as it is with an 
increasing lead. 

It must be noted that the Gooch link-motion at full-gear 
does not give the valve the motion that it would have if the 
connection were made by an eccentric-rod to the head of the 
valve-spindle. In this respect the action of the Gooch link- 
motion differs from the Stephenson link-motion, which at full- 
gear acts like a plain slide-valve gear. The diameter of the 
valve-circle is, at full-gear, 

{^' -f B")^ — rfsin' ^ + 4" ^^^^ ^ ^ ^7 ^^^ ^ ^^^ ^ 



^ 



-\- CDs'" ^ -\- j^ sin' (^ =F 2y sin 8 cos S\ 



LINK-MOTION, 6 1 

which for the ordinary proportions of the link-motion is a trifle 
longer than r. Consequently the full-gear action of a Gooch 
link-motion with open rods is equivalent to that of a plain slide- 
valve gear with a little greater angular advance ; with crossed 
rods it is equivalent to the action of such a gear with a little 
less angular advance. The difference in each case, though not 
large, is appreciable. 

The Allan Link. — At the time when link-motions were 
first used, the curved surfaces of either the Stephenson or the 
Gooch link could be properly finished only with considerable 
difficulty and expense. To obviate this difficulty, a straight 
link was devised by Allan which had the general appearance of 
the Gooch link, but which had both the link and the radius- 
rod movable in such a way as to give a proper motion to the 
valve. This gear was intermediate between the Stephenson 
and the Gooch link-motion ; for example, it had a variable lead, 
though the variation was less than with a Stephenson link 
having like proportions. With modern machine-tools and shop 
methods, there is no especial difficulty in finishing the curved 
surfaces of links, and the Allan link has consequently fallen into 
■disuse. 

Comparison of the Stephenson and Gooch Links. — 
A comparison of the link-motions on Plates XIII and XIV 
with that on Plate XVIII will show that the Gooch link-motion 
has more parts and more joints at which lost motion will 
result from wear, and that it occupies nearly twice the longitu- • 
dinal space required for a Stephenson link-motion. As an 
offset may be urged its property of giving a constant lead. 
The choice of a link-motion for a specific purpose must depend 
on the importance that should be attached to any given feature 
of the gear under the given conditions. With proper propor- 
tions either gear can be made to give the valve a nearly 
harmonic motion, or, with proper modifications, either gear 
may be adjusted to give an equalized cut-off; from this point 
of view neither appears to have an advantage. 



62 VALVE-GEARS FOR STEAM-ENGINES. 

A link-motion is used primarily to reverse the motion of 
the engine, and secondarily to give a variable cut-off ; under 
some conditions the second action is nearly if not quite as im- 
portant as the first. At one time link-motions under the con- 
trol of a governor were used to give an automatic cut-off on 
stationary, non-reversing engines ; and for such a purpose the 
Gooch link-motion was preferable because it imposed less 
friction on the governor. The weight of the Stephenson link- 
motion can be overcome either by counterbalancing or by 
speeding up the governor, and mass is rather advantageous 
than otherwise in that it steadies the governor ; but the fric- 
tion produced by the weight of the link and the eccentric-rods, 
and much more the friction of the gear, which is liable to be 
large and irregular, especially at the eccentrics and their straps, 
ought not to be imposed on a governor. The constant lead of 
the Gooch link-motion has been claimed as an advantage, and 
engine-builders usually so consider it ; but the discussion of 
this question in connection with shifting eccentrics, oji 
page 37, makes it clear that a decreasing lead is preferable 
for a stationary engine which has a variable cut-off with a 
single valve. Were this the only point under consideration,, 
the best result could be obtained by a Stephenson link-motion 
with long crossed rods, which would give a lead decreasing 
slowly toward mid-gear. Modern builders of stationary engines 
do not look favorably on the link-motion for an automatic 
cut-off gear. 

Reversing engines are of two types, those used on locomo- 
tive engines and those used on marine engines; the condi- 
tions of their service are so different as to merit detailed dis- 
cussion. Some stationary engines are reversing engines, and 
are controlled by hand instead of by a governor ; for examples 
may be mentioned winding and hoisting engines, and engines 
for driving reversing roll-trains. According to the conditions 
of their use, they will fall into one or other of the two classes 
mentioned, or may partake of the characteristics of both. 



LINK-MOTION. 63 

In starting a railway train, the link-motion is thrown into 
full-gear forwards, and should then give a long cut-off, so that, 
with the throttle-valve partially open, a moderate and steady 
force may be exerted on the driving-wheels to overcome the 
friction of, and impart motion to, the train, without slipping 
the wheels on the track. The lead may properly be small at 
full-gear, and is sometimes zero or even negative. As the 
train gets under way and the revolutions per minute become 
high, the action of the reciprocating parts becomes important ; 
just as was seen to be the case for a high-speed stationary 
engine (see page 36) there must be a considerable amount of 
compression in order that the engine may run smoothly. An 
early admission and release are also desirable in order that the 
steam may be supplied and exhausted freely. All these con- 
ditions are met by raising the Stephenson link toward mid- 
gear and opening the throttle-valve, and at the same time the 
economic advantage of the expansive working of steam can be 
obtained. 

American and English locomotive-designers have used the 
Stephenson link-motion, while Continental designers have used 
the Gooch link quite widely. In American practice the cylin- 
ders are commonly placed outside of the locomotive-frames, 
with the valve.-chest on top ; the link-motions are placed be- 
tween the frames and act on the valve through a rocker, as 
has already been shown on Plate XIII. English locomotives 
frequently have the cylinders inside the frames, and the valve- 
chests are on the sides of the cylinders and under the smoke- 
box ; the link-motions then act directly on the valve-spindle, 
using a link like that shown by Fig. 3, Plate XIII. When the 
Continental locomotive-designers use the Gooch link-motion, 
they place it outside the drivers, and so readily find room for 
eccentric-rods and radius-rod. Such a disposal of the valve- 
gear keeps it in sight where it may receive attention, but does 
not meet with favor among American and English engineers, 
since it is liable to derangement from slight accidents. 



64 VALVE-GEARS FOR STEAM-ENGINES. 

At the present time marine engines are commonly com- 
pound or triple-expansion, and the link-motions are used only 
for reversing the engine, the reverse arc having only three 
notches, full-gear forward, full-gear backing, and mid-gear. 
Crossed rods may be used to advantage, for then the engine 
can be stopped by setting the link at mid-gear. In this con- 
nection it may be remarked that an engine controlled by a 
Stephenson link-motion with open rods will not necessarily stop 
when the link is placed in mid-gear, provided the engine is 
running und^r no load or a very light load ; though the engine 
will not start with the link in that position. The normal con- 
dition for a marine engine is to run at full speed and under a full 
load, and when the speed decreases the load falls off rapidly^ 
The result of an attempt to adjust the steam-supply to a 
smaller load, by shifting the link toward mid-gear, is to give 
an excessive compression, and an early release, when the re- 
ciprocating parts have least effect, and when the reduced quan- 
tity of steam is readily exhausted. Simple-expansion engines 
and many compound engines were provided wath an independ- 
ent cut-off valve on the back of the main valve, of a type to 
be discussed in Chapter V. 

Locomotive link-motions have the pins and other smaller 
wearing parts made of hard steel, the link is case-hardened^ 
and the eccentric-rods are bushed with steel ; the eccentrics 
and straps are the only exception to the rule that all the wear- 
ing parts are made as hard as possible. With the exception of 
the eccentric-straps, no provision is made for taking up wear ; 
when the looseness becomes excessive the whole gear is over- 
hauled, and new pins and bushings provided if necessary* 
The reason for this practice is twofold : first, the complication 
of adjustable parts is avoided ; second, the gear is unavoidably 
exposed to dirt and grit, and when grit gets into a joint between 
a hard and a soft metal, it becomes embedded in the latter and 
rapidly abrades the hard surface. The custom is to equalize 
the cut-off by a method that gives a good deal of slipping of 



link-motion; 65 

the block in the link, but as both link and block are hard, and 
the cut-off is continually varying, this practice is not so ob- 
jectionable as it would be on a marine-engine link-motion. 

Marine-engine link-motions are designed to give the re- 
quired cut-off for full load when set at full-gear ; as has already 
been said, there is frequently no provision for shortening the 
cut-off as on locomotives. Since the engine is liable to run 
for days or weeks at full-gear forward, the gear is designed to 
give very httle slipping of the block in the link at this position. 
As the gear is large and frequently massive, the complication 
of making the wearing parts adjustable is not objectionable; 
and as the engine works in a closed engine-room, there is no 
reason why grit should get into the wearing surfaces, which 
may therefore be lined with soft metal when that is desirable. 

Modification of the Link-motion. — In the discussion of 
link-motions, hitherto, it has been supposed that the arrange- 
ment of the parts and the choice of dimensions have been 
such as to give a nearly harmonic motion to the valve. In 
both the Stephenson and the Gooch link-motions the link-pins 
are supposed to be on the link-arc ; in the first the radius of 
the link-arc is assumed to be equal to the length of the eccen- 
tric-rod, and in the second it is assumed to be equal to the 
length of the radius-rod. It is, however, possible by modify- 
ing some of the arrangements to obtain certain desired effects, 
such as the equalization of the cut-off, without sacrificing the 
equality of the leads. The effect of some of the modifications 
can be proved, or at least inferred, from the diagram of the 
link-motion ; but since they are in the nature of adjustments 
and must in any case be worked out by trial, it will be suffi- 
cient to state some of them for the Stephenson link-motion. 

Link-pins. — The link-pins of a Stephenson link-motion 
with a rocker may advantageously be placed back of the link- 
arc; withoitt a rocker they should be on the link-arc, or they 
may be placed ahead of the arc if mechanical difficulties do 
not interfere. 



66 VALVE-GEARS FOR STEAM-ENGINES. 

Saddle-pin. — By proper location of the saddle-pin, or the 
point of attachment of the hanger or bridle, it is possible to 
equalize the cut-off at any point of the stroke both in forward 
and backing gears. This element of the link-motion is by 
far the most effective, for good or evil, of all that the designer 
has at his control, and fortunately he usually has complete 
control over it. If a symetrical gear is desired, the saddle-pin 
should be placed at the middle of the length of the link; 
with a rocker it will be back of the link-arc, and without a 
rocker it will be ahead of the link-arc. With proportions 
common for American locomotives a fair action may be had 
by placing the saddle-pin at the middle of the link and half- 
way between the chord and the arc. On such locomotives, 
with a rocker, the slip of the link-block is greater in forward 
than in backing gear, when the saddle-pin is at the middle of 
the link ; and the forward-gear slip may be diminished by 
placing it nearer the forward-gear eccentric, but this is 
attained at the expense of the symmetry of the gear. Some- 
times the link is supported from below instead of being sus- 
pended from above ; and in such case the forward-gear slip is 
less than the slip in backing gear. Links for marine engines, 
and in English locomotives without a rocker, are frequently 
suspended by the forward link-pins. It is customary to equal- 
ize the cut-off at half-stroke or earlier, by a proper location of 
the saddle-pin ; in this book an equalization at one-third stroke 
will be made. 

Reverse-shaft. — The position of the reverse-shaft is often 
fixed, or susceptible of but little change. If it can be located 
at pleasure, it may also be used to equalize the cut-off at any 
point of the stroke. When so used, the location of the reverse- 
shaft is used to equalize the cut-off near the end of the stroke, 
usually in combination with an equalization of the cut-off by the 
location of the saddle-pin at half-stroke or earlier. With a rocker, 
such a manner of locating the reverse-shaft is liable to bring it in 
conflict with the eccentric-rods at one of the full-gear positions. 



LINK-MOTION. 6y 

Radius of the Link-arc. — It has been shown that the Hnk- 
arc for the Stephenson Hnk should have a radius equal to the 
length of the eccentric-rod, in order that the leads may be 
equal. It may sometimes be desirable to use a different radius 
to facilitate the equalization of the cut-off. Without a rocker, 
the radius may be made greater than the length of the eccen- 
tric-rod, and with a rocker it may be made less. Such a choice 
of the radius of the link-arc will sacrifice the equality of the 
leads, and the deviation from the normal radius must never be 
enough to badly derange them. In this connection it should 
be said that the lead near mid-gear supplies a large portion of 
the steam admitted, and that the lead at full-gear affects the 
facility with which the engine passes the centres ; much 
inequality in either place is undesirable. With open rods, the 
full-gear lead is small, and may vary from a certain amount to 
double that amount, or to zero, without serious consequence. 
At and near mid-gear the lead is large, and may vary as much 
absolutely as at full-gear, since that will not be much rela- 
tively. 

The motion of the valve will be more nearly harmonic with 
long rods and with a long link; the first should be twelve times 
and the second four times the eccentricity, or more, except 
under peculiar conditions. A skilful designer may use the 
inequality introduced by short rods or a short link to adjust a 
link-motion, but these dimensions are commonly fixed, and 
the modification of them for that purpose is not in general to 
be regarded with favor. 

Designing Link-motions. — The design of a link-motion 
may be divided into two parts : first, the choice of such a type 
of link-motion and such general proportions as will be likely 
to give a satisfactory solution of the problem in hand ; and, 
second, the application of modifications and adjustments to 
give equal cut-off, or to reduce the slip, or to produce any 
other desired effect. The first part of the design may be 
much aided by the use of the Zeuner diagram ; the second 



68 VALVE-GEARS FOR STEAM-ENGINES. 

part is commonly attained either by drawing out the link- 
motion and by making the proper constructions, or by aid of 
a working model with adjustable parts. A combination of the 
methods of drawing and using a model, combining certain 
advantages of each, will be explained later. The first part of 
the design is often so fixed by the requirements of the general 
design of the engine, or by custom, that it is liable to be 
neglected. 

Marine-engine Link-motions. — As has already been 
stated, the link-motions of modern marine engines are com- 
monly used for reversing only, and not for regulating the 
power of the engine. Since the Stephenson link-motion at 
full-gear acts like a plain slide-valve gear, the determination of 
the eccentricity and angular advance and the design of the 
valve may be carried, out by the methods given in the first 
chapter. It is customary to make the head-end lap greater 
than the crank-end lap, thereby partially equalizing the cut-off, 
and the consequent inequality of leads (the crank-end lead 
being the larger) is a partial compensation for the longer cut- 
off at the head end. In Fig. i, PI. V, the only change required 
is to choose the point of cut-off for both forward and return 
strokes, the former being the longer. 

The link is usually guided by the go-ahead pin, as shown 
on Plate XIV and Plate XIX, both of which represent the 
link-motion of the U. S. S. Maine \ though sometimes a point 
beyond the link-pin, or a point at the middle of the link, is 
chosen. This particular link-motion actuates a piston-valve 
like that shown by Fig. i, PL VII, which takes steam in the 
middle and exhausts at the ends. Consequently the motion of 
the valve is in the opposite direction from that of a plain 
slide-valve, and the general effect is like that produced by 
moving a valve through a rocker ; the eccentric follows the 
crank, and the rods are crossed, as shown on Plate XIV and 
Plate XIX. Let / and P be the positions of the go-ahead 
link-pin when the crank is on crank-end and head-end dead- 



LINK-MOTION, 69 

points respectively ; then with / and P as centres and with a 
radius equal to the length of the bridle, arcs are struck inter- 
secting at iV, which is one extreme pdsition of the end of the 
reverse-shaft arm. The length of the bridle is such that the 
arc aPpa^ nearly coincides with the line XX' , and the slipping 
of the link-block is small ; the arc aa^ is extended both ways 
for sake of clearness in the diagram. 

The location of the reverse-shaft may now be made either 
to give the backing action symmetrical with the forward 
action of the link, or to reduce the slip in backing-gear. 

Symmetrical Action. — Let it be assumed that the backing- 
link pin shall be guided to the points P and p, when the 
engine is on the dead-points ; then the go-ahead link-pin will 
be found at P^ and/^. With these points as centres and with 
the length of the bridle for a radius, draw arcs intersecting at 
71 ; and with N and n as centres and with the length of the 
reverse-shaft arm as a radius, draw arcs intersecting at S\ the 
last point is the desired location of the reverse-shaft. 

Reduction of the Slip. — In full-gear forward the go-ahead 
link-pin moves on the arc aa^^ and the backing link-pin 
describes an elongated looped figure, of which the upper loop 
is quite small ; P' and p' are two points on the larger loop. 
If now the link be thrown into full-gear backing, and if the 
backing link-pin be made to move on the line XX\ then the 
go-ahead link-pin will describe a looped figure of which P^ and 
p^ are two points. To draw the looped figure, let 6^ be a given 
position of the crank, and let E and E' be the corresponding 
positions of the eccentric-centres; with E' as a centre and 
with the length of the eccentric-rod for a radius, cut the line 
XX' at P\ with ^ as a centre and with the same radius, draw 
an arc and intersect it with another arc drawn from P and 
with the length of the link between the pins for a radius; then 
P^ at the intersection of the two last arcs is one point on the 
looped figure. To find other points, make the same construc- 
tion for a sufificient number of crank-positions, say twelve. 



*JO VALVE-GEARS FOR STEAM-ENGINES. 

at equal intervals around the circle described by the crank- 
pin. 

Find by trial a centre n^ , from which, with a radius equal 
to the length of the bridle, the arc tt^ may be drawn through 
the middle of the looped figure. Then with a radius equal to 
the length of the reverse-arm, draw arcs intersecting at S^ ; 
this is the location of the reverse-shaft for giving as small a 
slip as possible in full-gear backing. With this construction 
the go-ahead Hnk-pin describes the arc //, when the link is in 
full-gear, and at the same time the backing link-pin describes a 
looped figure similar to the one at P'p' ^ and lying partially on 
one side and partially on the other side of the line XX' near 
Pp. The link-block will slip in the link an amount nearly 
equal to the width of the looped figure P ^p^ , measured on a 
radial line from n^ ; the exact amount of slip can be found by 
drawing the true looped figure near /^ ; it is omitted in the 
diagram to avoid confusion. It is evident that the slip of the 
link-block will be greater if the construction for symmetrical 
action resulting in the location of the reverse-shaft at 5, should 
be used. In that case the slip is nearly equal to the total 
deviation of the looped figure P-^p^ from the arc through P^^p^ ; 
it can be found by drawing the true looped figure near /^ when 
the path of the go-ahead link-pin is the arc P^p^. 

Adjusting the Cut-off. — The distribution of work among 
the cylinders of a compound or multiple-expansion engine de- 
pends on the ratio of the volumes of the cylinders and on the 
cut-off for the several cylinders. If the distribution of the 
work is not satisfactory when all the links are set at full-gear, 
it may be adjusted, or at any rate it may be improved by 
shortening the cut-off on one or more of the cylinders. On 
recent marine engines, which have only three notches on the 
reverse-arc, namely, full-gear forward, full-gear backing, and 
mid-gear, a device known as a gag is put on the end of the re- 
verse-arm for this purpose. The rod of the bridle is carried 
by a block iV (Fig. i, PI. XIV), which may be moved in a slot 



LINK- MO TION. 7 1 

JVM'm the end of the reverse-shaft arm, by aid of a screw and 
hand-wheel, and thus the link may be moved toward mid-gear 
and the cut-ofT may be shortened. 

The construction of the gag for the link-motion shown on 
PL XIV is found on PI. XIX. A line is drawn midway be- 
tween nP^ and np^ , and perpendicular thereto is drawn the Hne 
njn; this is chosen as the centre-line of the slot and screw NM^ 
Fig. I, PI. XIV. In full-gear forward the centre-hne of the 
slot and screw is at MJV, which makes an angle of about 7° 
with a line midway between iVPand Njf. It is apparent that 
when the block iV is moved toward M, PI. XIV, the cut-off is 
shortened for forward-gear without changing the method of 
supporting the link-motion, while in backing gear the cut-off 
is not affected. If the slot should be placed at M^N, rn'riy 
making the angle PNM' equal to i8o°— P,;^;;/, then the cut-off 
will be shortened the same amount in both forward and back- 
ing gears ; but with such a construction the method of support- 
ing the link in forward gear will be affected by the action of 
the gag, and slipping of the link-block may then occur. 

Locomotive Link-motions. — In American practice the 
link-motion is set to give equal lead at full-gear, and is ad- 
justed to give equal cut-off ; the reduction of sHp being con- 
sidered to be of less importance, though it is not to be neg- 
lected. The adjustment of the cut-off is made by aid of a 
model with adjustable parts, by aid of which an experienced 
designer can readily work out a satisfactory motion, or at any 
rate as good a motion as the conditions will allow. 

In equalizing the cut-off, it is to be borne in mind that any 
irregularity at short cut-off is of much more importance than 
at long cut-off, since the amount of steam admitted to the 
cylinder is nearly proportional to the length of the cut-off, and 
the work varies with the amount of steam admitted. Thus an 
inequality of half an inch in six inches is -j^j, while half an inch 
in eighteen inches is only -gig-. 

The full-gear or maximum cut-off varies with the condi- 



']2 VALVE-GEARS FOR STEAM-ENGINES. 

tions of the service and the judgment of the designer from | 
to W of the stroke. When an engine, for example one in 
passenger service, is to be run at high speed and with a short 
cut-off, it is advisable to make the full-gear cut-off as short as 
the ready handling of the engine, when starting, will permit, in 
order that a favorable action of the valve may be obtained at 
short cut-off. This will be made clear by a comparison of Fig. 
4, PL XVI, in which the maximum cut-off is at \ of the stroke, 
with Fig. I, PI. XX, in which the maximum cut-off is at |- of 
the stroke ; the diameters of the full-gear valve-circles are the 
same. In each figure OP^ is the valve-circle for the link-block 
half-way between the link-pin and the saddle-pin. In Fig. 4, 
PI. XVI, OP^ has a diameter of ff of an inch, gives a maxi- 
mum port-opening of W of an inch, and the cut-off occurs at 
0.70 of the stroke. In Fig. i, PL XX, the cut-off occurs at 
0.55 of the stroke, the diameter of OP^ is ig^^ of an inch, and 
the maximum port-opening is again W of an inch. The com- 
parison also shows the importance of the first part of the de- 
sign of a link-motion, mentioned on page 6j, and the advan- 
tage of using Zeuner's diagram for that purpose. 

Skeleton ModeL — The author has found that a skeleton 
model, such as is shown on PL XX, can be used with advan- 
tage in laying out and adjusting a link-motion. It consists of 
a piece shown by Fig. 3 to represent the crank and eccentrics, 
of a template shown by Fig. 4 to represent the link, and of 
rods to represent the eccentric-rods, the hanger and the re- 
verse-shaft arm, together with screws and washers to make at- 
tachments. The several parts may be made of any fine-grained 
hard wood, such as mahogany or cherry. Fig. 5 shows one of 
the joints with a thick wooden washer, as at the eccentric-cen- 
tre /. A wood screw of proper size is cut off so that it may 
not protrude through the plate into which it is set. The hole 
at b for the screw is drilled a trifle smaller than the shank of 
the screw at the bottom of the threads, and a pointed screw 
like the one to be used is run through to cut a thread in the 



LINK-MOTION. 73 

hole. The hole in the washer c may be an easy fit for the 
screw, while the hole in the rod ^ is a snug fit for the body of 
the screw under the head. The countersunk hole in the rod 
d should be made with a tool like a machinist's countersink, 
but with the cutting edges sharper. The drilling and counter- 
sinking should be done in a lathe, or by some other method 
that will give true and straight holes. After the holes are laid 
out, a sharp-pointed centre-punch may be used to start the 
drill at the proper point. All the work on the model should 
be done exactly and thoroughly. 

In anticipation of laying out the model, a Zeuner's diagram 
should be drawn as in Fig. i ; in which the full-gear valve- 
circle OP is laid out as for a plain slide-valve to give the 
lead-angle XORa and the cut-off at OR^ corresponding to the 
piston-position a, on the assumption of harmonic motion. As 
was found to be the case for a plain slide-valve, it maybe neces- 
sary to modify and redraw the full-gear valve-circle in order to 
get a desired lead and lap. The diameter of the mid-gear 
valve-circle may be conveniently calculated by aid of the equa- 
tion (33), and then the locus PP^P^P^ of the end of the valve- 
circle diameters may be drawn as the arc of a circle centred 
on the line XX'. 

The crank template (Fig. 3) may now be laid out by draw- 
ing the axes OR and YOY, and laying out ^ and E' with the 
eccentricity and angular advance found in Fig. i. At i? a slip 
of brass is let into the under side of the template, or a slip of 
card-board is gummed onto the under side ; and the axis OR 
is drawn across the slip for a reference-mark. If card is used, 
it is well to gum a piece to the centre at (9, so that the tem- 
plate may turn smoothly. The line OR represents the crank, 
and may be conveniently six inches long for all models what- 
ever the true length of the crank of the engine. Holes are 
drilled at E and E' to receive screws, and a hole at O is drilled 
and countersunk for a screw-head. 

The link template (Fig. 4) has the divcjk cut to the radius 



74 VALVE-GEARS FOR STEAM-ENGINES. 

of the link-arc. mq is a diameter at the middle of the arc, and 
jp and kp' are parallel lines on which the link-pins / and p' are 
laid out, at a proper distance back of the arc. Holes are 
drilled at / and p' to receive screws. 

The rods which serve as eccentric-rods, hanger, and reverse- 
shaft arm are laid out with the proper lengths, and are drilled 
and countersunk as may be required. The latter is made wide 
enough to receive a weight to hold it in place during the use 
of the model. 

Washers will be required at e\ p', m\ and N, Fig. 2. 

On a drawing-board or drawing-table of proper size, spread 
a sheet of paper large enough to receive the model, and make 
constructions shown by Fig. 2. If desired, two smaller sheets 
may be used, one for the crank and eccentrics, and one for the 
link and the path of the cross-head. On the paper lay down a 
Xm^XX' for the axis of the drawing, preferably by aid of a long 
steel straight-edge. From the centre O draw a circle to repre- 
sent the path of the crank, with a radius equal to OR, Fig. 3. 
With a pair of beam compasses take off the length of the con- 
necting-rod to the same reduced scale as is used for the crank 
OR, and with the ends of the diameter R^ and i?/ for centres 
cut the axis XX' at x and x\ the ends of the path of the cross- 
head pin. Divide the path of the cross-head into fractional 
or decimal parts, or into inches, to the chosen reduced scale, as 
may be desired. Connect the eccentric-rods to the crank tem- 
plate and the link template, reserving the hanger and reverse- 
shaft arm till the saddle-pin is located. 

Full-gear Lap and Lead.— Set the model at a dead-point 
with the link-pin/ on the axis XX' as shown by Plate XIII, 
and mark the intersection of the link-arc with the axis XX' ; 
place the model on the other dead-point, / on XX', and again 
mark the intersection of the arc with the axis ; thus locating 
the points c and c'. Since the valve-displacement at a dead- 
point is equal to the lap plus the lead, cc' is twice Oc, Fig. I. 
Make on equal to on' equal to the lap ; then, whenever the link- 



LINK- MO TION. 7 5 

arc is on one of the points n or n\ the displacement of the 
valve is equal to the lap, and it is either at admission or at 
cut-off. 

Location of the Rocker. — The axis of the rocker is on a 
line oT perpendicular to the axis XX' at the point o. In order 
that the admission and cut-off may not be disturbed by the 
action of the rocker, the axis T may be so chosen that an arc 
from T shall pass through n and n' . For convenience in lay- 
ing out and erecting the engine, oT maybe made equal to the 
length of the arm of the rocker ; in that case n and ;/ are on an 
arc drawn through o, and at a horizontal distance from oT 
equal to the lap. 

Location of the Saddle-pin. — The location of the saddle- 
pin is commonly under the entire control of the designer, and 
should be so chosen as to give the best general action of the 
link, bearing in mind that an inequality at short cut-off is more 
deleterious than at long cut-off. It Avill in general be found 
advisable to equalize the cut-off at or near one-third stroke by 
aid of the saddle-pin. 

In order that the cut-off may be equalized at one-third stroke 
by this means, a preliminary location of the reverse-shaft is 
necessary ; this may be made by placing 5, the reverse-shaft 
axis, at a distance above XX' equal to the length of the hanger, 
and at a distance to the left of o equal to the length of the re- 
verse-shaft arm. On Plate XX 5 is a little further to the left 
for a reason to be explained later. From the preliminary loca- 
tion of the reverse-shaft as a centre draw an arc, such as N,N^. 

With the length of the connecting-rod, to the reduced 
scale, as a radius, and with points at one-third stroke on xx' 
for centres, draw arcs cutting the crank-pin circle at R and R', 
to find the crank-positions corresponding. Bring the reference- 
mark on the crank template to one of these points, as at R' 
for the return stroke, and put a weight on the template to hold 
it in place. Slip the link template up or down on the paper 
till the link-arc comes to the point n\ and mark the extremities 



76 VALVE-GEARS FOR STEAM-ENGINES, 

of the line 7n'q' on the paper and draw a bit of the arc ; drop 
the link template out of the way and draw a line connecting 
the yomtsm' and q\ This part of the construction is indicated 
on Plate XX, with the rods and templates in full lines. Bring 
the reference-mark of the crank template to R, and slide the 
link template up or down till the link-arc comes to n ; mark 
and draw the line mq together with a bit of the arc. This part 
of the construction is drawn on the plate with dotted lines, 
showing the link template and the centre-lines of the eccentric- 
rods. 

With the length of the hanger as a radius, find by trial a 
point on the arc N^N^ from which an arc may be drawn which 
shall intersect the lines mq and in'q' at points m and m\ at 
equal distances from the portions of the link-arc drawn at the 
forward extremities of those lines. This part of the work must 
be done with great nicety, and the surface of the paper should 
not be defaced by drawing unnecessary lines. 

Having the distance of the saddle-pin back of the link-arc, 
the location may be laid out on the link template, and a hole 
drilled to receive the screw at the end of the hanger. 

Location of the Reverse-shaft. — Though the location of 
the reverse-shaft, as has already been stated, may be used as 
an element for the adjustment of the link-motion, it is fre- 
quently out of the power of the designer to change it enough to 
produce much effect, and in general a good action of the link 
may be had without doing so. A small change in the location 
of the reverse-shaft has little effect on the action of the link ; 
consequently it may be made to suit the necessities or conven- 
ience of the general design of the engine, within limits ; for ex- 
ample, it is convenient to have S at some definite distance from 
Oy measured in inches and such fractions of an inch as are in 
common use in the shop. 

On Plate XX the reverse-shaft is so located that the hanger 
may swing through equal angles forward and back of the ver- 
tical, when the link is in mid-gear. This is accomplished by 



LINK-MOTION. 77 

making oi equal to the distance back of the link-arc, and then 
by drawing in^ and n^S vertical and horizontal, and equal to 
the lengths of the hanger and reverse-shaft arm respectively. 
When the reverse-shaft is thus located, the path of the saddle- 
pin at full-gear is not level, but is inclined upward a little at 
the end nearest the crank, something like the arc m^in^ Fig. 2, 
PI. XXI, though to a less degree. This is beneficial so far as 
the cut-off is concerned, though it is likely to increase the slip. 
It is probable that the cut-off maybe further improved in some 
cases by setting the reverse-shaft still further towards the axle 
O. Again, the reverse-shaft may be set further forward and so 
distribute the inequality due to the curvature of the path n^n 
of the upper end of the hanger. 

Finally, it may be stated that in general it will be sufficient 
to locate the reverse-shaft as far above the axis XX' as the 
length of the hanger, and as far back of 0, the mid-position of 
the link-block, as the length of the reverse-shaft arm ; or the 
preliminary location already stated may be made definite at the 
beginning. 

If it is considered advisable to use the location of the 
reverse-shaft to adjust the link-motion, then it may be made 
to equalize the cut-off at some point near the end of the stroke 
(for example, at f of the stroke) after the location of the saddle- 
pin has been used to equalize the cut-off at or near \ of the 
stroke. The construction is as follows : Place the reference- 
mark on the crank template at R^, Fig. 2, PI. XXI, the crank- 
position corresponding to f stroke forward, and bring the arc 
of the link-template to the point n ; then mark the line niaqa 
and the position m^ of the saddle-pin. Place the reference- 
mark of the crank template at i?j, the crank-position corre- 
sponding to f return stroke, and bring the link-arc to the point 
n'\ then mark the line mjqj and the location of the saddle- 
pin mj. Make similar constructions in backing gear, thus 
locating the points mi, and m/, the positions of the saddle-pin 
at cut-off at f stroke for the forward and return stroke ; or, 



78 VALVE-GEARS FOR STEAM-ENGINES. 

since the diagram in backing gear will be symmetrical with 
that for forward gear, the points m^, and tn^ may at once be laid 
off above the axis XX' symmetrical with the points nia. and w/. 
With the length of the hanger for a radius, and with iHg, and 
tnj, as centres, draw arcs intersecting at N^ ; and with the same 
radius and with ntj, and ?;^/ as centres, draw arcs intersecting at 
Ni. Again, with the length of the reverse-shaft arm as a radius 
and with the points N^ and iV^, as centres, draw arcs intersect- 
ing at S'\ this is the desired location of the reverse-shaft. It 
is to be noted, first, that such a location of the reverse-shaft 
is liable to derange the cut-off at \ stroke, and that con- 
sequently the saddle-pin must be relocated ; and second, that 
the axis of the reverse-shaft is thrown down so that it is liable 
to conflict with the eccentric-rod. 

Lead, Port-opening, and Slip. — After the locations of the 
saddle-pin and reverse-shaft are completed, the model is then 
to be used to test the action of the link in all grades forward 
and backing. To do so, connect up the reverse-shaft arm and the 
hanger ; place the reference-mark on the crank-template, at the 
crank-position corresponding to a chosen piston-position (for 
example, at half-stroke forward) ; adjust the link-template so 
that its arc shall come to the point n, Fig. 2, PI. XX ; and place 
a weight on the reverse-shaft arm. Turn the crank template 
and thus move the model till the link template comes to the 
point n'\ note the position of the reference-mark on the crank 
template, and find and record the corresponding position of the 
cross-head on its path xx' . 

With the same setting of the model find the lead, port- 
opening, and slip. The first will be found by placing the crank 
on the dead-points. The second must be found by noting the 
greatest displacement of the link-arc from n toward the rights 
and from n' toward the left ; these quantities are to be meas- 
ured on a horizontal chord, not on the arc, since they repre- 
sent the valve-displacements minus the lap. To find the slip, 
find and mark the highest point on the link-arc that comes to 



LINK-MOTION. 79 

the arc through nn\ and also the lowest point ; the distance 
between these points is the slip of the link-block. 

This investigation of the action of the link should be car- 
ried on systematically for a sufficient number of points of the 
stroke, and recorded in a table similar to that on page 82. 

Should the action of the link-motion be deemed unsatisfac- 
tory, experiments may be made by changing the various di- 
mensions of the link, so far as possible, following the general 
directions on page 65. It is probable that the most trouble- 
some element will be the slip of the link-block due to the at- 
tempt to equalize the cut-off, and with the method of suspen- 
sion shown on Plates XIII and XX this is worse in forward 
than in backing gear. When feasible, this unfortunate condi- 
tion may be reversed by supporting the link from below, with 
which arrangement the slip in forward gear will be less than 
in backing gear. 

Modifications of the Model. — The model as described is 
made in an inexpensive and yet a thoroughly serviceable man- 
ner, and with proper care may be kept in constant use for sev- 
eral days before the joints begin to show looseness. If condi- 
tions warrant, with a little care in design and expense in con- 
struction, and with the use of metal bearings and of devices for 
taking up wear, a model can be made, on the same general 
plan, that may serve for an indefinite time. It does not appear 
necessary to go into the details of such changes at this place. 

One of the most obvious changes, and one that is necessary 
if the pin is to be re-located, will be to provide some way of 
adjusting the saddle-pin ; for example, it may be placed on a 
block that can be slid and clamped on the link template. 

In certain positions of the model the eccentric-rod ep, Fig. 
2, PI. XX, strikes the washer at /. This difficulty may be par- 
tially removed by cutting a notch in the rod as at v, and by 
cutting the washer flat on one side as shown by the line ab, Fig. 
5. If desired, another notch may be cut at w, and the rod 
may be reversed end for end, thereby still further removing 



80 VALVE-GEARS FOR STEAM-ENGINES. 

this source of trouble ; but the screws at e and / are liable to 
become loose if they are taken out and reset many times. 

In case the link-pins are on the link-arc, the attachment of 
the rods may be made by aid of brass plates, screwed to the 
link template and drilled for screws that must be set into the 
ends of the eccentric-rods. 

If the link is supported from the go-ahead link-pin, as is. 
common in English locomotive practice, then the conditions 
will be found to be similar to those for a marine-engine link- 
motion shown on Plate XIV, and the equalization of the cut- 
off, if attempted, must be made by the location of the reverse- 
shaft. 

A skeleton model may readily be devised for adjusting and 
investigating the action of the Gooch link-motion. 

To Set a Link-motion. — If a link-motion is designed for 
equal lead, it is set by a method like the first method for set- 
ting a slide-valve with equal lead. Place the link at full-gear 
forward ; with the proper angular advance as near as may be 
for each eccentric, and with the engine on a dead-point give 
the valve the proper lead ; turn the engine into the other dead- 
point, and if the valve does not then give the proper lead, 
change the length of the eccentric-rod by half the error, and 
shift the eccentric till the proper lead is obtained. Place the 
link at full-gear backing and set the valve again, changing the 
length of the eccentric-rod and the angular advance as may be 
necessary. Now place the link again at full-gear forward, and 
see if the setting has been disturbed by the changes of the 
backing eccentric and eccentric-rod ; if it has, the valve must 
be reset by the same method. Place the link again in full-gear 
backing, and make any correction needed ; very commonly 
none will be required. When a link-motion is designed to give 
unequal leads (a common practice on marine engines), the 
process differs only in that the lead at each end must be made 
the proper amount. 

The second method given on page 30 cannot be used in 



LINK-MOTION. 8 1 

setting a link-motion, since the maximum port-openings are 
not likely to be equal. 

When a rocker is employed with a link-motion, the length 
of the valve-spindle should be such that the arm of the rocker 
shall swing equal angles on each side of a perpendicular through 
its axis, to the central line or axis of the link-motion ; but a 
little divergence from this condition will not have much effect. 

The eccentric-rods for the Hnk-motions on Plates XIII and 
XIV are joined to the eccentric-straps by T-heads and bolts. 
The length of the rods may be adjusted by placing slips of 
metal called shims under the head — a method which may ap- 
pear crude, but is really convenient and effective. The bolt- 
holes through the shims can be slotted through to one side in 
order that a shim may be put in or withdrawn without taking 
the bolts out. 

Application of Skeleton Model.— To illustrate the method 
and to show the influence of changing some of the parts of a 
link-motion, there are given here the results of the application 
of the skeleton model to a few examples. 

The following dimensions were used in all the examples : 

Eccentricity 3 inches. 

Outside lap f ** 

Radius of link-arc 48 " 

Length of hanger 16 " 

Length of reverse-arm 20 " 

Length of rocker- arm (when used) 12 " 

Stroke „ 12. " 

Ratio of crank to connecting-rod 1:5 

In all the examples except that shown by Table II the dis- 
tance from the centre of the eccentric to the link-arc was equal 
to the radius of the link-arc ; the length of the eccentric-rods 
from the centre of the eccentric to the link-pins v/as made 
less or more than this distance according as the link-pins were 



82 



VALVE-GEARS FOR STEAM-ENGINES. 



back of or ahead of the link-arc, except for the example shown 
by Table V, which had the link-pins on the link-arc. The 
saddle-pin in all cases is at the middle of the length of the 
link. Other dimensions of the link-motion and details of the 
arrangement are given with the tables. 

TABLE I. 

Rocker used — link-pins 2| inches back of link-arc. 
Cut-off equalized at \ stroke. 
Saddle-pin ^ of an inch back of link-arc. 
Distance between link-pins 14 inches. 



Cut-ofE. 


Lead. 


Slip. 


Travel. 


Port 
Open- 
ing. 


a 
H.E. 


b 
C.E. 


Diff. 
a &.b 


6 


5il 


1 


1 5 


\ 


H§ 


15 


9 


8if 


1 


tV 


t\ 


2tV 


il 


12 


III 


i 


tV 


i 


o23 


1 


15 


HH 


1% 


H 


1 1 


3tV 


f 


18 


i7f 


f 


f 


i 


3M 


I^ 


21 


20f 


f 


^V 


i 


4f| 


Ifi 


22i 


22 


i 


tV 


H% 


6A 


2f^ 



In this example the reverse-shaft was set square, i.e. with 
the arm horizontal at midgear as shown on PI. XX, and the 
cut-off was equalized at -J stroke only. It may be considered 
to be the typical example. The lead at full-gear, or with the 
cut-off at 22|- inches, is small, but increases rapidly as the cut- 
off is shortened, till it is nearly half an inch when the cut-off is 
at quarter-stroke ; meanwhile the travel and port-opening both 
decrease rapidly. The travel of the valve in full-gear is more 
than twice the eccentricity, due to the slip of the link-block 
and to other irregularities. 

An inequality in the cut-off of J of an inch in 24 inches, 
i.e. one per cent of the stroke, cannot be distinguished in the 



LINK- MO TION. 8 3 

running of the engine or on the indicator-diagram; consequently 
the cut-off may be considered to be equalized from i to f of 
the stroke. The inequahty of the cut-off becomes as large as 
f of an inch at 18 and 21 inches ; but while such an inequality 
may possibly be distinguished on an indicator-diagram, it can- 
not have an appreciable effect on the running of the engine. 

In all the examples the gear was made symmetrical ; conse- 
quently the action in backing gear was almost identical with 
that in forward gear, and need not be stated separately. 

TABLE II. 

Rocker used — link-pins 2'^ inches back of link-arc. 
Cut-off equalized at \ stroke. 
Saddle-pin ^ of an inch back of link-arc. 
Distance between link-pins 14 inches. 



Cut-ofE. 


Lead. 


Slip. 


Travel. 


Port 
Open- 
ing. 


a 
H.E. 


b 
C.E. 


Diff. 
a Sib. 


6 


5fl 


^ 


1^ 


i 


2t^ 


15 


9 


Sfl 


A 


1^ 


i 




1 7 


12 


I If 


\ 


M 


■h 


ol 1 


f 


15 


Hit 


^ 


f 


f 


z-h 


H 


18 


i7f 


f 


li 


i 


3^ 


I^ 


21 


20f 


1 


i 


M 


4il 


Ifi 


22i 


22^ 


H 


H.E.i 
C.E.-^ 


li 


6A 


m 



In this example the eccentric-rods were made one inch 
longer than in the preceding example, which made the radius 
of the link-arc one inch shorter than required for the normal 
condition, i.e. 48 instead of 49 inches. The effect was to re- 
duce the inequality of the cut-off at long cut-off, so that the 
cut-off may be considered to be practically equal for the entire 
stroke. The full-gear lead had an inequality of yV ^^ ^^ ^^^^» 



84 



VALVE-GEARS FOR STEAM-ENGINES. 



but at other grades of the Hnk the lead was sensibly equal. 
Had the link been set to give equal lead at full-gear, then the 
mid-gear lead would have had an inequality of yL of an inch in 
half an inch, which would not have any appreciable effect in 
the running of the engine. 



TABLE III. 

Rocker used — link-pins 2f inches back of link-arc. 
Cut-oflf equalized at ^ stroke and at full-gear. 
Saddle-pin -f^ of an inch back of link-arc. 
Distance between link-pins 14 inches. 



Cut-off. 


Lead. 


Slip. 


Travel. 


Port 
Open- 
ing. 


a 
H.E. 


b 
C.E. 


Diff. 
a Sl b. 


6 


5li 


M 


tV 


9 

3¥ 


-7I3 
233 


tV 


9 


8ff 


3 

3^ 


T^^ 


t\ 


2i 


i 


12 


12 





if 


if 


2| 


f 


15 


14M 


1 
33 


f 


i 


3t6 


29 
33 


18 


^m 


A 


5 

1^ 


li 


3t 


ItV 


21 


io\\ 


tV 


T% 


I 


4il 


If 


22^ 


22M 


3% 


H.E. 
C.E.-jV 


li 


6i 


2^ 



In the third example the cut-off was equalized at |- stroke 
and at full-gear as recommended by Auchincloss in his Link 
and Valve Motions^ by the method described on page 77 and 
shown on PI. XXI. With the ratio of crank to connecting-rod 
used in these examples, i.e. 1:5, the reverse-shaft was found 
to interfere with the eccentric-rods at full-gear backing. The 
table shows that the equalization of the cut-off was nearly per- 
fect from half-gear to full-gear. The inequality in the cut-off 
increases as the cut-off is shortened, that is, at the place where 
it has the most deleterious effect ; but it must be admitted that 



LINK-MO TION. 



8S 



an inequality of f of an inch in 6 inches cannot have a very 
bad effect, if indeed it should be distinguishable in the run- 
ning of the engine. Both the danger of interference of the 
reverse-shaft with the eccentric-rods and the inequality of cut- 
off near mid-gear will be found to be less with a more favorable 
ratio of crank to connecting-rod, or with the cut-off equalized 
at \ and •§ stroke as recommended on page 77 and shown on 
PL XXI. 

TABLE IV. 

Rocker used — link-pins 3 inches back of link-arc. 
Cut-off equalized at \ stroke. 
Saddle-pin ff of an inch back of link-arc. 
Distance between link pins 12 inches. 



Cut-off. 


Lead. 


Slip. 


Travel. 


Port 
Open- 
ing. 


a 
H.E. 


b 
C.E. 


Diff. 
a&b. 


6 


51 


i 


f 


f 


2t"S- 


1 3 

T2" 


9 


m 


tV 


f 


1 1 
T6- 


2M 


if 


12 


iiH 


■h 


'^ 


f 


2f 


^ 


15 


Hf 


f 


^ 


If 


2il 


f 


18 


i7f 


f 


-h 


il 


3i 


I 


21 


20| 


f 


^ 


l\ 


4il 


If 


22i 


22 


i 


H.E. ^^ 
C.E.-^V 


If 


61^ 


2tV 



The fourth example had the reverse-shaft set square and 
differed from the first example in that the link was made 
shorter, i.e. 12 instead of 14 inches between the link-pins ; the 
link-pins were also set back 3 inches instead of 2f, but such a 
change has not much effect. A comparison of this table with 
Table I will show that shortening the link increases the ir- 
regularities of the link-motion, and especially that it increases 
the slip at all gears. 



2>6 



VALVE-GEARS FOR STEAM-ENGINES. 

TABLE V. 

Link acts directly on valve-spindle without rocker. 

Link-pins on link-arc. 

Cut-off equalized at ^ stroke. 

Saddle-pin \ of an inch forward of link-arc. 

Distance between link-pins, 12 inches. 



Cut-ofiE. 


Lead. 


Slip. 


Travel. 


Port 
Open- 
ing. 


a 
H.E. 


b 
C.E. 


Diff. 
a&Lb. 


6 


6f 


8 

8 


f 


3 

T6 


2t\ 


13 
"ST 


9 


9iV 


1 
T6- 


f 


^ 


ol3 


if 


12 


I If 


i 


s 

8 


\ 


.7I9 
2^2" 


1^ 


15 


I4f 


f 


w 


5 

T6 


2f 


H 


18 


i7i 


1 


1 1 

32 


3 

8 


3f 


H.E. I 

C.E.I- 


21 


20A 


if 


7 
"3^ 


i 


4t 


H.E. If 
C.E. l\ 


22i 


21^ 


f 


-h 


f 


6tV 


H.E. 2f 
C.E. 2,% 



This example was chosen to represent the type of link-motion 
which acts directly on the valve-spindle without the interven- 
tion of a rocker, and, as is customary, has the link-pins on the 
link-arc. It may be compared with Table IV, which has the 
link-pins the same distance apart. The equalization of cut-off 
from i to f stroke is good, though not perfect, and the inequal- 
ity at and near full-gear cannot have a very bad effect, though 
it is much larger than in the fourth example. The slip is less 
than for that example at all grades ; but probably the slip 
could be much reduced in such a link-motion with a rocker, if 
the link-pins were placed nearer the link-arc or on the link-arc. 
Such an arrangement would show greater inequality in cut-off 
than is found in Table IV. 

The sixth example was chosen to show the effect of placing 
the link-pins ahead of the link-arc, on a link which acted direct- 



LINK-MOTION. 



87 



ly on the valve-spindle without the intervention of a rocker. 
Such an arrangement would require the use of a side-bar link 
or a box link (shown by Fig. i, PI. XIV, and Fig. 3, PL XVIII), 
and might involve some mechanical difficulties. 



TABLE VI. 

Link acts directly on valve-spindle without rocker. 

Link-pins 3 inches ahead of link-arc. 

Cut-off equalized at \ stroke. 

Saddle-pin if of an inch ahead of link-arc. 

Distance between link-pins, 12 inches. 





Cut-off. 


















Lead, 


Slip. 


Travel. 


Port 
Open- 
ing. 


a 
H.E. 


b 
C.E. 


Diff. 
a &. b 


6 


6f 


f 


3 

8 


t23 
^3¥ 


23V 


8 

8 


9 


Q31 
^3 2^ 


sV 


f 


iH 


2f 


1^ 


12 


I HI 


1 

1 6 


1 1 


t3 1 


2f 


tV 


15 


I4f 


i 


^ 


t21 
^32 


2if 


fi 


18 


I7H 


1^ 


i 


If 


3i 


1 


21 


20H 


-h 


3 

TB" 


If 


4f 


lA 


22-1- 


22f 


i 


h 


If 


6| 


2H 



The equalization of the cut-off must be considered to be 
satisfactory, but it is attained at the expense of an excessive 
slip of the link-block. Probably a compromise between the 
link-motions shown by Tables V and VI, having the link-pins 
an inch or an inch and a half ahead of the link-arc, would be 
found to give a fair equalization of the cut-off without exces- 
sive slip. Also greater distance between the link-pins (14 in- 
stead of 12 inches) could be used with advantage. 



CHAPTER IV. 
RADIAL VALVE-GEARS. 

The name radial valve-gear has been applied to a number 
of reversing-gears that differ widely in detail and in general ap- 
pearance, but agree in that they derive the mid-gear motion of 
the valve from some source that is equivalent to an eccentric 
with 90° angular advance, and they combine with this motion 
another that is equivalent to that of an eccentric with no angu- 
lar advance. The general conception of this form of valve- 
gear is most easily obtained from an example. 

Walschaert Gear. — This gear is chosen as the first ex- 
ample of the type because the elements are easily distin- 
guished. In Fig. I, Plate XXII, H is the engine cross-head, 
and a is the head of the valve-spindle. The valve is moved 
through a radius-rod, one end of which carries a block that 
may be set at any position in a slotted link dF, and the other 
takes hold of a combining-lever af^ that receives motion from 
the engine cross-head. The slotted link swings on a fixed 
trunnion at G and is moved by an eccentric OE, which has no 
angular advance. In Fig. 2 the diagram in thin lines shows 
the gear at a dead-point, and the diagram in heavy lines 
shows the gear when the crank has moved through the angle 

Cfic= e. 

If the motion of the engine cross-head can be considered to 
be harmonic, then it is clear that the motion that it gives to 
the valve could be derived from an eccentric with 90° angular 
advance ; this motion is made equal to the lap plus the lead. 



RADIAL VALVE-GEARS. 89 

If the block d is at the middle of the link, the valve will derive 
motion from the cross-head only and the mechanism will be at 
mid-gear. The radius of the link-arc is made equal to the 
length de of the radius-rod, consequently the lead is constant 
for all settings of the gear. If the point h of the guiding-link 
hf were a fixed point, then the valve would receive motion 
from the eccentric OE^ which has no angular advance. By 
placing the link-block nearer the trunnion G the motion is 
reduced ; for example, the motion communicated from the 
eccentric OE will be half as much if the block is half-way be- 
tween d and G, If the link-block is below G the motion is 
reversed. 

The displacement from mid-position of a valve moved by 
an eccentric is 

^ = r sin (^ -[- <^). 

Now the motion derived from the cross-head is equivalent to 
that from an eccentric having 90° angular advance, provided 
the cross-head motion is assumed to be harmonic. Conse- 
quently the valve derives a displacement from this source of 

e^ = r, sin {6 -|- 90°) = r^ cos d. ... (53) 

From the proportions of the combining-lever and the length 
R of the crank, we have 

ae „ 

The displacement of the valve from the influence of the 
eccentric OE is 

e^ = r, sin {0 -\- 0°) == r, sin 6^, . . . . (54) 

in which 

dG af 

' GF ef 



90 VALVE-GEARS FOR STEAM-ENGINES. 

The entire displacement e of the valve at any crank-angle 
is the sum of the displacements from the two independent 
sources. 

.-. e = e^-\- e^ = r^ cos 6^ -|- r^ sin 6^ ; . . . (55) 

and since r^ and r, are constant for any grade of the link, 
equation (54) is a special case of equation (29), r^ and r^ being 
the coordinates of the diameter of a valve-circle for that grade 
of the gear. 

In Fig. I, Plate XXI, the valve-circle OP^ is drawn with a 
diameter r^ and represents the mid-gear action of the valve. 
The circles Op, Op^ , and Op^ represent the motions derived 
from the eccentric OE^ at full-gear and at two intermediate 
gears. The circles OP, OP^, and OP^ represent the actual dis- 
placements of the valve, derived from both sources. It is evi- 
dent that 



OP = \0P, + Op 



[*> 



and that OP^ and OP^ may be obtained in a similar manner* 
A comparison of Fig. i, PI. XXI, with Fig. 3, PL XVII, shows 
that the action of the Walschaert gear is equivalent to that of 
the Gooch link-motion. To aid in this comparison, the dimen- 
sions OP^ and P^P were transferred from Fig. 3, PI. XVII, ta 
Fig. I, PL XXI, and consequently the diagrams are identical. 

As actually constructed, this gear does not give harmonic 
motion to the valve, for the motion of the cross-head of the 
engine with the usual proportions of locomotives has consid- 
erable irregularity from the angularity of the connecting-rod ; 
also some irregularity is introduced by the combining-lever a/. 
Consequently such a diagram as Fig. i, PL XXI, can be of use 
only in roughly blocking out a gear. The real action of the 
gear can be determined either by constructing diagrams similar 
to Fig. 2 on as large a scale as convenient, or by aid of a modeL 



RADIAL VALVE-GEARS. 9 1 

A combination of the two methods, similar to the skeleton 
model for link-motions, may be found convenient for this pur- 
pose. Since part of the motion of the valve is derived from 
the cross-head, the adjustment of the gear to give equal cut-off 
will generally be easier than for a link-motion. 

In laying out a Walschaert gear, the combination-lever af 
should be made vertical when the cross-head is at the middle 
of its stroke ; the guiding-link hf should be made to vibrate 
equal angles above and below a horizontal line ; a line from G 
to F Qw the link should be made vertical when the engine is on 
a dead-point; and the supporting-link with the reverse-arm ST 
should be so laid out that it may be guided nearly on a horizon- 
tal line, unless the adjustment may be found to require a differ- 
ent arrangement. The length of the combining-lever should 
be so chosen that its angular vibration shall not exceed 60°. 

The main dimensions of the gear for any engine will be 
imposed on the designer by the general proportions of the 
engine and its frame. There are, however, two elements over 
which the designer will have more or less control : they are the 
position of the axis of the trunnion G, which in the figures is 
on the link-arc, but which may be placed either forward of or 
back of the link-arc ; and the reverse-shaft T, which may often 
be located at will, within limits. The first will be found to have 
the most influence on the action of the gear. 

The eccentric OE is sometimes replaced by a return-crank 
from the engine-crank C. The link is sometimes turned the 
other way, in which case the radius-rod extends forward from 
the head of the valve-rod. 

Marshall Valve-gear. — Plate XXIII shows the Marshall 
valve-gear as applied to the U.S.S. Yorktown. In Fig i, XX' 
is the axis of the cylinder, O is the centre of the shaft, and C 
is the crank-pin. The eccentric centred at E gives motion to 
a short and massive eccentric-rod EG, which is guided at o 
by the link oDy and is connected to the valve-spindle K by a 
valve-rod GV, The guiding-link oD is supported by the bell- 



92 VALVE-GEARS FOR STEAM-ENGINES. 

crank lever DoSj having its axis at o ; the rod ST gives con- 
nection with the reverse-shaft arm TU. In the figure the 
engine is at a dead-point, so that the guided point of the 
eccentric-rod coincides in projection with the axis of the bell- 
crank lever. 

Fig. 2 shows the centre-lines of the gear in two positions ; 
the heavy lines are for the full-gear of the valve-motion, and 
the fine lines are for a gear between that and the mid-gear. 
OC is the centre-line of the crank ; E is the centre of the 
eccentric; FD is the guiding link; and oD is the arm of the 
bell-crank lever, having its axis at o. 

When the bell-crank lever is set to give the mid-gear action 
of the valve, D is found at D^ , and the guided point F moves 
on an arc of a circle that nearly coincides with the line OV; 
the point E describes a circle, and all other points of the 
eccentric-rod describe ovals that are more or less elongated as 
they are near or removed from the guided point F. In this 
setting of the gear the horizontal motion of the point G is 
made equal to the lap plus the lead, so that the valve receives 
a motion like that given by an eccentric having 90° angular 
advance ; as 6^ is beyond F, the eccentric E properly coincides 
with the crank. 

At any other gear than mid-gear, for example with D set 
for full-gear, the vertical displacement of F will have two 
-components, one along the axis OV, and one perpendicular to 
it. The second component with some modification is trans- 
ferred to G and gives to the valve an additional displacement 
like that from an eccentric with no angular advance. This 
gear is consequently of the general type described at the be- 
ginning of the chapter, but the various irregularities of the 
gear are so marked that the valve-diagrams similar to Fig. i, 
PI. XXI, cannot be used at all in designing and laying out the 
gear. Since the guided point i^is always brought into coin- 
cidence with the axis of the bell-crank lever when the engine 
is on a dead-point, the lead is the same for all gears. 



RADIAL VALVE-GEARS. 93 

The cut-off is shortened by making D approach D^ ; the 
thin lines show the gear set for a cut-off at about f stroke. 
The engine is reversed by carrying D beyond D^ toward D" . 

Fig- 3 gives the valve-ellipses for full-gear and for a short 
cut-off, corresponding with the diagrams in full lines and finer 
lines shown by Fig. 2. The valve-ellipses show the defect of 
the gear, which is a marked inequality in the maximum port- 
opening. In spite of this defect, the gear has been much used 
for horizontal marine engines, as it interferes less than would 
a link-motion with the access to the working parts of the 
engine when running. 

In some cases the point G is taken between the eccentric 
and the guided point, in which case the eccentric is set oppo- 
site the crank. 

The design of the Marshall valve-gear must be carried out 
by the aid of diagrams or a model, or by a combination of the 
two methods, which appears to be well adapted for this work. 

Hackworth Valve-gear. — This gear differs from the Mar- 
shall gear in having the guided point carried by a block that 
slides in straight guides and thus avoids the irregularity due 
to the guiding-link. The irregularity of the valve-motion is 
less than when the Marshall gear is used, and the maximum 
port-openings can be made nearly equal. The pressure on the 
sliding-block is large, especially at full-gear, and unless ample 
wearing surface is provided the friction and wear are liable to 
be excessive. In some cases the sliding-block has been pro- 
vided with rollers to reduce the friction. 

Joy Valve-gear. — An example of the Joy valve-gear used 
on the Pennsylvania Railroad Company's tugboat Delaware is 
shown by PI. XXIV. XX' is the centre-line of the crank and 
connecting-rod, and xx' is the centre-line of the valve-spindle. 
The lever abc is guided on a flat arc by the rod go, and is 
attached to the connecting-rod at the point a^ which describes 
an oval having the length a^a^ equal to the stroke of the engine. 
This oval, which is omitted to avoid confusion of the diagram. 



94 VALVE-GEARS FOR STEAM-ENGINES. 

is symmetrical with regard to the axis XX' j and is slightly 
more pointed at the cross-head end than at the crank end. 
The point ^, which describes the irregular oval bb^b^ , takes the 
place of the centre of the single eccentric used with the 
Marshall valve-gear (PI. XXIII), and acts on the lever bze. 
The point t of the lever bie is guided on the circular 2.x o, ff^ 
by the sliding-block B^ and the point e^ which describes the 
oval ee^e^ , carries the valve-rod ed. The connecting-rod CD^ 
the valve-rod ed, and the rod eg are in one plane ; the levers 
ac and be and the curved guide-bar ^^ are double, one system 
being on each side of the connecting-rod ; in the figure the 
system of levers in front of the connecting-rod is omitted to 
show the construction more clearly. The guided point i could 
evidently be guided on the arc ff^ by a link centred at k \ 
such a construction is frequently used in marine engines. A 
comparison of this gear with the Marshall valve-gear will show 
much similarity. The essential points of difference are : (i) the 
radius of the guiding-arc ff^ is always equal to the length of . 
the valve-rod, and (2) the irregularity due to the angularity of 
the lever bie is compensated by the action of the lever ac, 
somewhat in the manner that the linkage known as Watt's 
parallel motion is made to give nearly a straight-line motion. 
These advantages are attained at the expense of greater com- 
plication and cumbersomeness ; in passing it may be remarked 
that the inequality of port-opening, which is the notable defect 
of the Marshall gear, may be nearly if not quite remedied by 
making the length of the guiding-link equal to the valve-rod, 
but such a construction is usually impracticable since it requires 
either an impossible length for the guiding-link, or else a short 
valve-rod and a long valve-spindle that must be guided at the 
outer end. The guiding-bars _//"i are hung on trunnions with 
the axis at the point i^ , and are connected at/" to the reversing- 
lever. The gear is shown at full-gear for left-handed rotation ; 
it may give a shorter cut-off if the guiding-bars ff^ are given 
less inclination from the horizontal or mid-gear position, and 



RADIAL VALVE-GEARS. 95 

when in mid-gear it will give the valve a motion equal to the 
lap plus the lead ; if the guiding-bars //"^ are inclined the other 
way the engine will be reversed. 

This gear, when properly proportioned, gives a rapid motion 
to the valve when opening and closing, less compression at 
short cut-off than does a link-motion, and the cut-off can be 
made nearly equal for all grades of the gear. Like all other 
radial valve-gears, it gives a constant lead. Its defects are, 
the number of parts and of joints that are liable to wear loose, 
and the obstruction that it offers to inspection and care of the 
crank-pin and cross-head when the engine is running. 

To lay out a Joy valve-gear : choose a point a on the con- 
necting-rod, having a transverse throw equal to twice the maxi- 
mum displacement of the valve ; make the length of the lever 
ac such that the angle a^c^a^ shall not be more than 90° ; draw 
the centre-line xx'' of the valve-gear, and locate the point e^ op- 
posite the middle-point of the line a^a^\ lay off e^e^ = e^e^ equal 
to the lap plus the lead ; lay off aj)^ = aj)^ equal to about one 
third of a^c^ ; and draw the lines ej}^ and ejb^ intersecting at i^ : 
this last point locates the axis of the trunnions carrying the 
guiding-bars ff^. If the point i is guided by a link, then the 
arm carrying the link must be centred at i^ ; in the figure the 
position of such an arm is shown by the line ij^. Finally, the 
valve-ellipse should be drawn for several grades of the gear; 
in the figure the valve-ellipse 00^ has its length equal to the 
stroke of the engine, and the valve-displacements are magnified 
fourfold, i.e. st = /\d^d. Usually the axis xx' of the valve- 
motion is determined by the general design, and cannot be 
changed much, if at all. The length of the lever ac will com- 
monly be as great as desirable if the angle a^cjj^ is something 
less than 90° ; it cannot be made shorter without throwing ex- 
cessive stress on the links and levers. The transverse motion 
of the point a is properly twice the maximum displacement of 
the valve, in order that the inclination of the guide-bars //"^ 
may not be more than 25° or 30°; should such a location 



9^ VALVE-GEARS FOR STEAM-ENGINES. 

bring the lever ac too near the shaft, as may be the case when 
the crank is counterweighted, then a may be placed nearer 
the cross-head, but at the expense of more inclination of the 
guiding-bars at long cut-off. The location of the point b is 
under the control of the designer, and may be used to equalize 
the cut-off either at that grade at which the engine is to run 
habitually, or el^e to give nearly equal cut-off at all grades. 
The equalization of the cut-off must be made by trial, and no 
general rule can be given, since the elements, such as the length 
of the lever ac and the distance between the axes xx' and XX' y 
over which the designer has little control, have a large influ- 
ence. A skeleton model may be used to advantage in this 
work. It should have rods to represent the connecting-rod, 
the levers ac and be^ and the links eg and ki. The point k 
will be located on an arc of a circle centred at i^ . The points 
i and b on the levers be and ac should be made adjustable ;: 
the first by mounting it on a sliding-block that can be clamped 
in any desired position, and the second by that method, or by 
a series of holes to receive the screw representing the pin at 
b. It may be found advantageous to provide pieces, properly 
guided, to represent the cross-head and head of the valve- 
spindle, but a simple model may be made by placing these 
points by hand on the lines XX' and xx' for the several po- 
sitions of the model, and the centre C may in like manner be 
placed on the circle CC'C* 



CHAPTER V. 
DOUBLE VALVE-GEARS. 

A PLAIN slide-valve, set to give an early cut-off, is liable to 
give either an excessive compression or an early release, or 
both. A single valve under the control of a gear that gives a 
variable cut-off, such as a shifting-eccentric or a link-motion, 
is open to the same difficulties ; and in addition the compres- 
sion varies with the cut-off, though to a less degree. For a 
stationary engine a large compression may be undesirable, and 
a varying compression is always so. To avoid these difficulties 
two valves are frequently used ; one, called the main valve, has 
an unvariable motion, and gives the admission, release, and 
compression ; the other, called the cut-off valve, gives the 
cut-off only, which may be varied without affecting the other 
events of the stroke. 

The cut-off valve may be placed in a separate valve-chest, 
as shown by Fig. 3, PI. XXV, or it may be placed on the back 
of the main valve, as shown by Fig. i, PI. XXVI ; thus giving 
rise to two separate types of double valve-gears. It is impor- 
tant to obtain a clear conception of the principles of double 
valves, and then all existing forms of double valve-gears may 
be readily understood, and a gear for a given purpose may be 
easily designed, or else it may be shown that a satisfactory 
design is impossible. 

Cut-off Valve in a Separate Valve-chest. — The usual 
arrangement of this valve-gear is shown by Fig. 3, PI. XXV. 
The main valve, which receives motion from an eccentric with 

97 



98 VALVE-GEARS FOR STEAM-ENGINES. 

constant angular advance and eccentricity, is designed to give 
the desired release and compression, and is set to give equal 
lead ; it will be observed that either the release or the com- 
pression may be equalized. In the figure there is no inside 
lap ; this arrangement may be frequently found desirable, but 
it is chosen here for the sake of simplicity, and will be adhered 
to throughout the chapter ; attention will be given exclusively 
to the cut-off, since the other features of the gear are the same 
as for a plain slide-valve and have received sufficient attention 
in the first chapter. 

In the figure the valves are shown disconnected from the 
eccentrics and both in mid-position ; they cannot both be in 
such position when the gear is connected up, but such a draw- 
ing is convenient in laying out the valves. The cut-off valve is 
a rectangular open frame having the acting edges inside. The 
distance / from one edge of the valve to the opposite edge of 
the port is the clearance of the valve ; when the valve is dis- 
placed from mid-position an amount equal to the clearance, 
the cut-off valve gives either cut-off or readmissio7i. The right- 
hand edge gives cut-off for the head end of the engine, and 
readmission for the crank end ; it is important that the read- 
mission by the cut-ofT valve should precede the admission by 
the main valve, in order that the second steam-chest shall then 
be properly filled with steam at full pressure. 

The steam-porj; a^ is for the passage of full-pressure steam 
only, and may consequently be made from |^ to f of the area 
of the port a, through which exhaust steam also must pass. 
Two or more ports are frequently provided in the cut-off valve- 
seat, and the valve is then known as a gridiron valve ; in such 
case the combined area of all the ports a^ should be a little in 
excess of what would be given to one port, to allow for the 
greater friction in numerous narrow passages. A gridiron valve 
acting on several narrow ports will require a proportionately 
less throw. 

In Fig I, PL XXV, OP is the diameter of the valve-circle 



DOUBLE VALVE-GEARS. 99 

for the main valve which gives admission at OR^ and OR^, and 
cut-off at OR. The eccentric acting on the cut-off valve is given 
a negative angular advance, i.e. it is less than 90° in advance of 
the crank ; consequently the displacements of the cut-off valve 
from mid-position are given by a valve-circle, such as OP^, hav- 
ing its diameter laid off at an angle 8^ (the negative angular 
advance) away from the crank. If the clearance is equal to 
(94, then the cut-off by the cut-off valve occurs at OR^ and 
the readmission at OR. 

A variable cut-off by aid of this gear may be obtained by 
varying the clearance of the valve, or the throw of the eccentric, 
-or by using a shifting-eccentric. Now the same effect is pro- 
duced by increasing the lap (or decreasing the clearance) with 
a constant eccentricity as is produced by decreasing the 
eccentricity with a constant lap ; consequently an investigation 
of one of the two methods will serve for both. It will appear 
that neither will give a good variable cut-off. On the other 
hand, a satisfactory gear may be had by using a shifting- 
eccentric. 

In Fig. I, PL XXV, the clearance 01^ gives cut-off at OR^ 
and readmission at OR, coincident with the cut-off by the 
main valve : and that is the latest admissible cut-off ; for if the 
•clearance is made equal to 01^ in order to obtain a cut-off at 
OR^ , the readmission will occur at OR^ , before the main-valve 
■cut-off, and a double admission of steam will occur. Such a 
double admission causes a large waste of steam and an irregular 
action of the engine and cannot be tolerated. The earliest 
admissible cut-off is obtained by a clearance equal to 01^, 
which gives cut-off at OR^ and readmission at OR^ . An in- 
spection of the figure shows that the angle RfiR^ must, from 
symmetry, be equal to ROR^\ the latter angle depends on the 
lap of the main valve, and it is at once evident that only a limited 
range of cut-off can be obtained with such an arrangement. 

In practice a gridiron cut-off valve was commonly used and 
the cut-off was obtained by varying the travel of the valve. 



100 VALVE-GEARS FOR STEAM-ENGINES. 

For this purpose a fixed eccentric was connected to the end of 
a slotted lever or link, and motion was communicated to the 
valve from a link-block that could be set at any desired place 
in the link. To shorten the cut-off, the link-block was moved 
toward the fixed end or fulcrum of the link. An idea of this 
arrangement may be obtained by supposing the radius-rod of 
the Walschaert gear (Plate XXII) to act on the cut-off valve^ 
spindle ; the eccentric should, of course, have a negative angular 
advance, and only half of the link will be required. The effect of 
such an arrangement is the same as though the eccentricity 
were varied, and, just as has been shown to be the case for a 
gear with varying lap, the range of variation of cut-off depends 
on the lap of the main valve. 

Cut-off Valve with Shifting-eccentric. — If the cut-off 
valve in a separate valve-chest is moved by a properly de- 
signed shifting-eccentric, the readmission may be kept within 
the proper limits, i.e. before the admission and after the cut- 
off by the main valve, and at the same time any desired range 
of cut-off may be had. 

In Fig. 2, PI. XXV, let OP be the main valve-circle, giving 
cut-off at OR and admission at OR^. Suppose that the cut-off 
is to vary from OR^ , corresponding with ■§• stroke, to OR co- 
incident with the cut-off by the main valve. Bisect the angle 
ROR^ by the line OP^, and bisect the angle ROR^ by the line 
OP^ ; then a valve-circle centred at 67/ can be made to 
give a cut-off coincident with that by the main valve, and 
readmission coincident with the main-valve admission ; while a 
valve-circle centred at C^ can give cut-off at OR^ , and readmis- 
sion coincident with the main-valve cut-off at OR. 

It is convenient to have the shifting-eccentric on an arm 
centred on the centre-line of the crank, or rather on that line 
produced, for then the cut-off gear will work equally well in 
forward and in backing gear on a reversing-engine ; but for 
a stationary engine such an arrangement is not essential. We 
now have three elements of which one may be chosen at 



DOUBLE VALVE-GEARS. lOI 

pleasure and the other two will then be determinate. In the 
figure the diameter OP^ of the valve-circle to give early cut-off 
is made if inches, equal to the eccentricity for the main 
eccentric ; the clearance 01 of the cut-off valve is then deter- 
mined by the intersection of that circle by the lines OR and 
OR^ , and is if of an inch. The centre C^ of the valve-circle 
to give the cut-off coincident with that of the main valve must 
be so chosen that it shall pass through O and I" ; it is on a 
perpendicular to 01" at its middle point. Draw AS perpen- 
dicular to the middle point of an imaginary line joining P^ and 
P/; then 5, the intersection of this line with the axis XX' , is 
the centre of an arc on which the point P^ will travel as the cut- 
off is shortened. The shifting-eccentric must be swung from a 
point on the centre-line of the crank produced, and at a distance 
from the centre of the shaft equal to OS (ij of an inch) ; when 
the crank is at OX this point will be at T. With ordinary 
proportions for an engine, the point 2"is liable to fall inside the 
shaft, or el^ so near that the construction of an arm for the 
eccentric will be impossible. A reversing-engine may have 
the following arrangement : fast to the shaft may be an eccen-^ 
trie with an eccentricity equal to OS and with its centre opposite 
the crank-pin ; this eccentric may carry another having an 
eccentricity equal to ^5 (if |- of an inch); the second or outside 
eccentric will be turned toward the crank so that its angular 
advance will be negative. A stationary engine that always 
runs in one direction may have the swinging arm, for the eccen- 
tric controlling the cut-off valve, centred at any convenient 
point on the line AS produced. 

There now remains the determination of the width of the 
cut-off valve to prevent leakage past the outside edge. The 
greatest displacement of the valve from mid-position is equal to 
OP^ = i|- of an inch ; consequently the distance in Fig. 3, PL 
XXV, from the outside edge of the valve to the nearest edge 
of the port should be somewhat greater than if of an inch ; it 
is made ly^- of an inch. 



102 VALVE-GEARS FOR STEAM-ENGINES. 

Cut-off Valve on back of Main Valve.— Fig. i, PL XXVI, 

shows a cut-off valve on the back of the main valve, both being 
disconnected from their eccentrics and placed in mid-position. 
When the gear is connected up, such a position of both valves 
at the same time does not occur, but it is convenient to make 
a drawing of the valves in that position to show the laps and 
other dimensions of the main valve, and the clearance and 
length of the cut-off valve. The main valve is designed to give 
the desired compression and release, and is set to give equal 
lead ; either the compression or the release may be equalized. 
The cut-off valve is connected to an eccentric having a large 
angular advance, so that it is nearly (sometimes exactly) op- 
posite the crank. 

In Fig. 3, OP is tlie diameter of the main valve-circle, and 
OPf^ is the diameter of a valve-circle showing the absolute dis- 
placements of the cut-off valve. At any crank-position, such 
as OR', the chord Oc intercepted by the main valve-circle shows 
the displacement of the main valve; represented in Fig. 2 by 
£. The absolute displacement of the cut-off valve is shown by 
the chord Ob, intercepted by the cut-off valve-circle ; repre- 
sented by e^ in Fig. 2. Both of these displacements are toward 
the left, but the former being the greater, the relative displace- 
ment e^ of the cut-off valve with regard to the main valve, and 
measured from the centre of the main valve, is towards the 
right, tending to shut the port in the main valve. 

Now the displacement of the main valve, with an eccen- 
tricity r and an angular advance d, is, for the crank-angle 6^ 

e = r sm{S -\- 6) = r sin 6 cos 6 -\- r cos d sin B. . (56) 

The cut-off valve-eccentric has the angular advance S^ and 
the eccentricity r^ , and for the crank-angle 6 the displacement 
of the cut-off valve is 

e, = r, sin {6^ -\- 6) = r, sin d^ cos ^ -f r„ cos 6^ sin 6. (57) 



DOUBLE VALVE-GEARS. IO3 

The relative displacement of the cut-off valve measured 
from the middle of the main valve is 

e^-=e—e^={r sin d— r^ sin d^ cos d-\-{^ cos d— r„ cos d^ sin d, (58) 
which may be written 

e^=^ A cos 6^ -|- ^ sin 6^ ^^M 

Now it has been shown on page 50 that any valve-motion that 
can be represented by an equation having the form of equation 
(59) is harmonic ; and can be represented by a valve-circle^ 
having for the coordinates of the end of the diameter of the 
valve-circle A and B. 

Since r„ cos S^ is longer than r cos S, A will in this case be 
negative and must be laid off to the left of the origin. Conse- 
quently the circle representing the relative motion of the cut- 
off valve may be located in Fig. 3 by laying off Ov = A and 
vP^ = B^ and then by drawing the diameter OP^ on which the 
circle is to be drawn. This circle is called the auxiliary circle ; 
it is to be borne in mind that the angle YOP^ is not an angular 
advance, nor is OP^ an eccentricity. 

Auxiliary Valve- circle. — Although the auxiliary valve- 
circle can always be drawn by the process just stated, the usual 
and convenient method is as follows : In Fig. 4, PI. XXVI, let 
OP and OP^ be the diameters of the valve-circles for the main 
valve and the cut-off valve ; with /* as a centre and with a 
radius equal to OP^ , and with 6^ as a centre and with a radius 
equal to PP^ , draw arcs intersecting at P^ ; then OP^ is the 
diameter of the auxiliary circle. The figure PxPPfi is of 
course a parallelogram, and the process just described will be 
called completing the parallelogram. 

To prove the method just given : Draw P^v and Pu parallel 
to OY, and draw Ps and Pj: parallel to OX. It is evident that 

Ov = P^u — Pj; — Ps =r^ sin d^— r sin 6 =: —A ; 
P^v = Pu = Os — Ot = r cos ^ — r^ cos S^ = B. 



104 VALVE-GEARS FOR STEAM-ENGINES. 

When the displacement of the cut-off valve from the middle 
of the main valve is equal to the clearance /, Fig. i, PI. XXVI, 
the edge of the valve coincides with the edge of the port and 
we have either cut-off or readmission. The crank-position at 
cut-off and readmission can be found by drawing the circle llj^ 
with a radius 01 equal to the clearance /. In Fig. 3 cut-off oc- 
curs at the crank-position OR^ , corresponding to a piston-dis- 
placement xa^ for harmonic motion ; the valves are then in the 
position shown by Fig. 6. Readmission occurs at OR'' ; the 
edge of the cut-off valve is on the edge of the port as in Fig. 6, 
but the valve is then moving towards the left to open the port 
through the main valve; the main valve is not in the position 
shown by that figure. It is important to know when cut-off by 
the main valve occurs ; in Fig. 3 it occurs at OR, correspond- 
ing, with harmonic motion, to a piston-displacement xa ; the 
valves are then in the position shown by Fig. 7. 

The readmission by the cut-off valve must not occur before 
cut-off by the main valve, otherwise a double admission of 
steam will take place. It should occur before the admission 
by the right-hand end of the main valve ; i.e., before the crank 
comes to the position ORa , Fig. 3. The readmission for the left- 
hand end of the main valve is of course given by the left-hand 
edge of the cut-off valve. 

Meyer Valve. — A double valve-gear, known as the Meyer 
valve, is shown by Fig. 2, PI. XXVIII. The cut-off valve is 
made in two parts on a valve-spindle with a right and left 
screw, so that the position of the plates may be adjusted 
by rotating the valve-spindle ; thus the clearance may be 
changed, and consequently the cut-off may be varied. In 
order that this may be done while the engine is running, there 
is a swivel-joint in the valve-spindle between the valve-rod 
head and the valve-chest, and the tail of the valve-spindle is 
carried through the head end of the valve-chest, where it 
reciprocates through a hand-wheel as shown by Fig. i ; the 



DOUBLE VALVE-GEARS, IO5 

valve-spindle is squared so that it may be rotated by turning 
the hand-wheel. 

In Fig. I, PI. XXVII, the valve-circle OP, the auxiliary 
circle OP^, and the diameter OP^ for the valve-circle showing 
the absolute motion of the cut-off valve, are transferred from 
Fig. 3, PL XXVI. The cut-off by the main valve occurs, as in 
that figure, at OR. With the same clearance 01, the cut-off 
by the cut-off valve is at the crank-position OR^ , 90° from the 
dead-point. If the clearance is increased to the amount 01^ , 
the cut-off is delayed and occurs at the crank-position OR^ . 
With this clearance the readmission occurs at OR, coincident 
with the cut-off by the main valve, and a later cut-off would 
be accompanied by a readmission ; consequently the latest 
admissible cut-off is at the crank-position OR^ . 

In order that cut-off may occur at a given crank-position, 
for example at OR^ corresponding to a piston-displacement 
-equal to Xa^ , the clearance must be made equal to the chord 
(7// = 01^ , cut from the line OR^ by the auxiliary circle. If 
the clearance becomes zero, so that in mid-position the edge of 
the cut-off valve coincides with the outer edge of the port in 
the main valve, then the cut-off comes at a crank-position 0R\ 
perpendicular to the diameter OP^ of the auxiliary circle. 
For an earlier cut-off, the line of the crank, for example OR^ , 
will cut the auxiliary circle at a point beyond the origin O ; 
and the cut-off valve will then have a lap equal to O// = 01^ 
when in mid-position. For a cut-off at the dead-point a lap 
equal to 01^ will be required. The crank-position at readmis- 
sion is at the second intersection of the auxiliary circle by the 
clearance-circle ; for example, with a clearance equal to 01^ , 
the readmission occurs at OR. When the valve has a lap in 
mid-position, for example 01^, the readmission occurs at a 
crank-position found by drawing a line from the second inter- 
section of the clearance-circle and the auxiliary circle, towards 
the origin O and thence to the crank-pin circle. The readmis- 
sion usually comes in the second or third quadrant, and so long 



I06 VALVE-GEARS FOR STEAM-ENGINES. 

as it is later than the cut-off by the main valve, it is of little 
importance to know just where it occurs. 

Design of a Meyer Valve. — The main valve shown by 
Fig. 2, PI. XXVIII, has an outside lap of half an inch, and 
is moved by an eccentric with an eccentricity of i J of an inch ; 
the inside lap is zero. It is set with -Jg- of an inch lead. With 
these dimensions the valve-circle OP in Fig. 3 can be drawn,. 
and the cut-off will be found to occur at ORc\ corresponding,, 
with harmonic motion, to 0.89 of the stroke of the piston. 

The steam-port in the valve-seat is f of an inch wide, and 
the steam-port through the main valve may be taken to be 
f as much, or \ of an inch. The diameter of the auxiliary 
circle may be assumed to be one inch. With an eccentricity 
of if of an inch for the cut-off valve-eccentric, the parallelo- 
gram PPfiP^ may be drawn locating both the auxiliary circle 
OP^ and the diameter OP^ of the circle showing the absolute 
displacements of the cut-off valve. The cut-off valve-eccentric 
has the angular advance YOP^, equal to 55°; it is convenient 
to know this angle approximately in setting the valves. The 
dimensions for OP^ and OP^ are chosen by trial to give a con- 
venient location of the auxiliary circle, with its diameter placed 
beyond OR^ . Were the auxiliary circle placed with its diam- 
eter coincident with OR^, as shown by Fig. 5, PI. XXVI, then 
a readmission would be impossible ; such a disposition is 
recommended by Zeuner, but it has the disadvantage that the 
motion of the cut-off valve is very slow when giving a long 
cut-off. This defect is mitigated by placing the auxiliary circle 
beyond OR^, as in Fig. 3, PI. XXVIII; the earliest possible 
readmission is clearly at OR^, 

The largest clearance is 01^ 01' = W of an inch; the 
least clearance, or the greatest lap, will depend on the earliest 
required cut-off. Let it be assumed that the earliest cut-off 
shall be at OR^ , corresponding to a piston-displacement Xa 
= -J of the stroke, for harmonic motion ; then the cut-off valve 
must have a lap equal to 01^ = 01 ^ =yV ^^ ^^^ inch, nearly. 



DOUBLE VALVE-GEARS. 10/ 

The lower face of the main valve is laid out as for a plain 
slide-valve, but with the additions demanded by the passage 
through it. The least width of bridge is equal to the eccentricity 
less the sum of the lap and the width of port, or i i — (i + f ), 
= i of an inch ; the width used is \ of an inch. In like 
manner the width of the exhaust-space is ij- + | — J = if of 
an inch ; the width used is 2 X t| = ij of an inch. In order 
that the edge c of the passage through the valve may not 
reduce the passage through the port to less than \ of an inch, 
the distance ac is made 1 4 H" i" = 2 inches; this feature is fre- 
quently overlooked and dc is carelessly made equal to ef. In 
order that the edge g of the valve shall not come to the edge 
b of the port, the distance bg is made ii-'+ |- = if of an inch. 
The valve-face is cut away at a point h, if of an inch from g^ 
thereby giving an overtravel of \ of an inch. In order that 
the space efdc may be made small, the height of the exhaust- 
space is made only ly^ of an inch, a dimension that is probably 
too small to give a perfectly free exhaust. 

The width of the cut-off valve must be enough so that 
steam cannot leak past the inside edge when the valve is set to 
give the earliest cut-off and also has its maximum displace- 
ment. In Fig. 2, PI. XXVIII, the position of the valve to give 
cut-off at \ of the stroke is shown by dotted lines ; its lap is 
^ of an inch, and its left-hand edge /^ is i -|- -J = i|^of an inch 
from e. The length of the cut-ofT valve is \\ -\- ^ -\- ^ ^=. 2-^-^ 
inches. The cut-off valve is shown in section with a clearance of 
W of an inch, which is proper for giving the longest cut-off coin- 
cident with that of the main valve ; its left-hand edge is 2^ 
-j- |i- =: 3gL inches from the edge /" of the port ef', the distance 
of the edge f of the port from the middle of the valve is 
made '^^-^ inches. The half-length of the main valve, over all, 
is made 4J inches, and provides an overtravel of J of an inch 
for the cut-off valve when set to give the earliest cut-off. 

The valve-spindle is provided with a right-and-left-hand 
screw, of which the right-hand part is shown. The thread 



I08 VALVE-GEARS FOR STEAM-ENGINES. 

should be cut only far enough to give the desired variation of 
cut-off, or some other stop should be provided in order that 
the engine attendants may not move the cut-off valve too far 
out, and so get a leakage or even admission of steam past the 
inner edge. The spindle is shown in two parts, joined by a 
right-and-left screw and circular nut or sleeve with pins to 
prevent the joint from jarring loose ; this arrangement is to 
facilitate the erection of the valve-gear. 

In this design the inside lap is made zero and the compres- 
sion and release are neglected ; in practice these features 
should receive the same attention as is accorded to them in 
designing a plain slide-valve. Again, the irregularity of the 
piston-motion due to the angularity of the connecting-rod 
has been ignored, and the clearance (or lap) of the cut-off 
valve has been made the same at both ends. This method is 
commonly followed in practice, but by using proper pitches 
for the threads on the valve-spindle the cut-off may be equal- 
ized at two points of the stroke, for example at ^ and at \ 
stroke, and will then be found to be more nearly equal for all 
parts of the stroke, except for long cut-off, when inequality is 
of less importance. 

Meyer Valve with Cut-off at Inside Edge. — Sometimes 
the Meyer valve is designed to cut off at the inside edge, as 
shown by Fig. 4, PI. XXVIII. It is then convenient to con- 
sider that the valve has a lap ab which diminishes as the cut- 
off is lengthened, and which may become zero and finally 
change to a clearance, shown by ac when the valve is in the 
position indicated by dotted lines. The eccentric is given a 
negative angular advance, i.e. it is set somewhat less than 90° 
ahead of the crank. 

In Fig. 2, PI. XXVII, the main valve-circle is (9P, giving 
a c'ut-off at ORy w^ith a lap On = On". Let it be assumed that 
the earliest required cut-off is at OR^ , and that the latest read- 
mission must be at OR^ ; then the auxiliary circle may have 
its diameter at OP^., on a line bisecting the angle R^OR^. Tiie 



DOUBLE VALVE-GEARS. IO9 

diameter of the valve-circle for showing the absolute displace- 
ment of the cut-off valve will be found at OP^ by completing 
the parallelogram PP^OP^\ the eccentricity for the cut-off 
valve-eccentric is OP^ , and the negative angular advance is 
YOP^. The auxiliary circle may be placed lower down, 
thereby giving an earlier readmission and at the same time a 
longer eccentricity, but it cannot be placed higher up. There 
is no danger of a double admission of steam at a long cut-off, 
as was found to be the case with the ordinary form of Meyer 
valve. 

Meyer Valve for Reversing-engines. — If a Meyer valve 
is designed to give a satisfactory action in forward gear for a 
reversing-engine, the backing gear is liable to be very unfavor- 
able. In Fig. 5, PL XXVI, the main valve-circle for forward 
gear is OP, and with a lap-circle nn'n" the cut-off comes at OR,^ 
corresponding to f stroke with harmonic motion. The auxil- 
iary valve-circle has its diameter coincident with OR^ to avoid 
the possibility of a double admission of steam ; the eccentricity 
is found to be equal to OP^, and the angular advance is equal 
to YOP^. In backing gear the main valve-circle is at OF , and 
cut-off by the main valve is at OR^ , corresponding to f stroke, 
but the auxiliary valve-circle is now OPJ' , found by complet- 
ing the parallelogram /*'Po 6^/*/'. With a clearance equal to (9/ = 
01' = 01" y the cut-off in forward gear occurs at half-stroke, 
but in backing gear the cut-off is at OR^ , corresponding to \ 
stroke. Such an arrangement cannot be used, for with it the 
engine cannot run at full power m backing gear. The action 
of the cut-off valve may be made the same in forward and 
backing gears by giving its eccentric 90° angular advance. In 
Fig. 5 the parallelogram PP\OPJ is drawn with PP^ parallel 
to ORc, and with PPJ parallel to XX', thus giving the diame- 
ter of the auxiliary circle coincident with OR^ and giving 
90° angular advance, but both the cut-ofT eccentricity and 
the relative travel of the valve are thereby made excessive. 
In practice the cut-off eccentric is often given the same eccen- 



no VALVE-GEARS FOR STEAM-ENGINES. 

tricity as the main valve-eccentric, and then with 90° angular 
advance it is liable to give a double admission at long cut-off. 

Cut-off Valve with Loose Eccentric. — Let the cut-off 
valve receive motion from an eccentric which may turn freely 
on the engine-shaft and which is under the control of a shaft- 
governor ; let the clearance of the cut-off valve be unalterable : 
then the cut-off can be varied by changing the angular advance 
of the cut-off eccentric. 

In Fig. 3, PI. XXVII, the main valve-circle is OP, and with 
a lap on = on' the cut-off by the main valve occurs at OR^^ 
The cut-off eccentric may have its angular advance changed 
from YOP^ to YOP^, and the auxiliary circle may change 
from OP^ to OPJ. When the position of the diameter OP^ 
of the circle showing the absolute displacement of the cut- 
off valve is known, the auxiliary circle may be located by 
completing the parallelogram PP^OP^\ or the centre Cx of the 
auxiliary circle may be located by completing a parallelogram 
CC^OC X on the half-diameters OC and OC^ of the main valve- 
circle and the cut-off valve-circle. Since the side CC^ of this 
last parallelogram is equal to OC^^^\OP^ , it is at once apparent 
that the locus of the centre of the auxiliary circle is the dotted 
circle C^CJ drawn from the centre C of the main valve-circle, 
and with a radius equal to half the eccentricity of the cut-off 
eccentric. Again, since PP^ is equal to OP^ , the locus of the 
end of the diameter of the auxiliary circle is a circle drawn 
from P as a centre and with a radius equal to the eccentricity 
of the cut-off eccentric. The locus of the centre of the auxil- 
iary circle is the more convenient for use in solution of prob- 
lems. 

Let it be assumed that the cut-off shall vary from the crank- 
position ORc , coincident with the cut-off by the main valve, to 
OR^ , corresponding to \ stroke for harmonic motion. Assume 
the clearance of the cut-off valve and draw the circle ll'l". 
Erect a perpendicular 5(7^ at the middle of the line 01" \ it 
will intersect the locus C^CJ at C^ . the centre of the auxiliary 



DOUBLE VALVE-GEARS. Ill 

circle that will give a cut-off by the cut-off valve coincident 
with the cut-off by the main valve. In like manner, erect a 
perpendicular at the middle of the line 01' ; it will locate the 
centre C^ of the auxiliary circle that gives a cut-off at OR^ , 
corresponding to \ stroke. In designing a valve-gear of this 
type, the clearance of the cut-off valve may be chosen, usually 
somewhat larger than the width of the port in the main valve ; 
and then the auxiliary circle for maximum cut-off may be 
given such a diameter that a satisfactory action may be had in 
that gear. The eccentricity of the cut-off eccentric will be 
found by completing the parallelogram in the usual way ; 
should the result be an undesirable dimension it may be modi- 
fied, since the diameter of the auxiliary circle may be varied to 
a considerable extent. Finally, the auxiliary circle to give the 
earliest cut-off may be found by the process just stated ; it is 
liable to have a large diameter, and the travel and wear of the 
cut-off valve is likely to be excessive. In the figure the auxil- 
iary circle which gives a cut-off at J stroke is one third larger 
than the main valve-circle, and it would be still larger for a 
shorter cut-off. The maximum diameter of the auxiliary circle 
is equal to the sum of the eccentricities for the two eccentrics. 

If this gear is used with a shaft-governor, the cut-off by the 
main valve will commonly be earlier than that shown in Fig. 
3 — a circumstance that will make the design of a satisfactory 
gear easier. Moreover it may be possible to limit the maxi- 
mum cut-off to half-stroke or less, even though the main valve 
gives a cut-off beyond half-stroke ; in that case the valve 
mechanism must be so arranged that the cut-off valve cannot 
act beyond the assumed range of cut-off, otherwise a double 
admission may occur. These observations are applicable also 
to the next type of valve-gear. 

Cut-off Valve with Constant Travel. — It is desirable that 
a valve shall overtravel its seat in order that the seat and the 
face of the valve may wear evenly and remain true. This is 
seldom possible for a Meyer valve with the common propor- 



112 VALVE-GEARS FOR STEAM-ENGINES. 

tions, or for the cut-off valve under the contro] of a loose 
eccentric. It has been seen that the design of the cut-off valve 
is conveniently begun by choosing the diameter and position of 
the auxiliary circle ; it will be found that the design of a double 
valve-gear for a given purpose may be worked out by first 
finding how the auxiliary circle must be located or changed to 
give the desired action, and then finding how the cut-off eccen- 
tric must move to produce such an auxiliary circle. 

Suppose that the auxiliary valve-circle is to have a constant 
diameter, and that the variation in cut-off is to be produced by 
swinging the auxiliary circle around the origin O, Fig. i, PL 
XXIX, from the position OP^ to OP^. With a clearance 
equal to (9/= 01' = 01", the first-named auxiliary circle will 
give cut-off at OR^ , coincident with the cut-off by the main 
valve ; and the other auxiliary circle, OP J, will give cut-off at 
OR^ , corresponding to \ stroke. The diameters of the cut-off 
valve-circles, showing absolute displacements, are OP^ and 
OP^, found by completing the parallelograms PP^OP^ and 
PPJOP^'. It is evident that the locus of the point P^ is the 
circle P^PJ drawn from P as a centre and with a radius equal 
to the diameter, of the auxiliary circle. 

The arrangement of the eccentrics for this type of valve- 
gear is shown by Fig. 2, PI. XXIX. The centre of the engine- 
shaft is at 6^ ; on the shaft is the fixed eccentric centred at Ey 
for giving motion to the main valve ; the cut-off eccentric is 
carried by the main eccentric, and is shown by the full-line 
circle with its centre at ^/, corresponding to OPJ in Fig. i, 
while the dotted circle shows it with the centre at E^ , corre- 
sponding to OP^ in Fig. i. The cut-off eccentric may readily 
be placed under the control of a shaft-governor. 

The main valve represented by Fig. 3, PI. XXIX, has a lap 
of ^ of an inch, and is moved by an eccentric having i^ of an 
inch eccentricity, and is consequently a reduplication of the 
main valve for the Meyer valve-gear shown on PI. XXVIII, at 
its lower surface ; the top is of course laid out after the cut-off 



DOUBLE VALVE-GEARS. II3 

valve has been designed. The main valve-circle has its di- 
ameter at OP, Fig. I, and the cut-off by that valve occurs at 
ORc. The cut-off valve is a double-ported or gridiron valve, 
each of the ports being \ of an inch wide. The clearance of 
the cut-ofT valve is assumed to be f of an inch, represented by 
the circle U'l" . As the auxiliary valve swings toward the right 
to give an earlier cut-off, the readmission moves through the 
same angle toward the line OR^, the crank-position at cut-off 
by the main valve ; and it is at once evident that the readmis- 
sion must not be earlier than ORcy otherwise a double admis- 
sion may occur. The smallest admissible auxiliary circle will 
have its centre on the line Os bisecting the angle R^OR^, and 
it will pass through the points I' and l'^ at the intersection 
of the clearance-circle by the lines OR^ and OR^. The diam- 
eter chosen for the auxiliary circle is f of an inch, or twice 
the clearance of the cut-off valve. The extreme positions, 
OPJ and OP^y of the auxiliary circle are so located that they 
shall pass, one through r and the other through l"\ they give 
cut-off at OR^ and at OR^. The corresponding diameters of 
the cut-off valve-circles are OP^' and OP^, found by complet- 
ing the parallelograms P^PP^O and PJPP^'O. The cut-off 
eccentric is mounted on the main eccentric and has an ec- 
centricity, referred to that eccentric, of J of an inch, equal to 
the diameter of the auxiliary circle. 

In laying out the cut-off valve and the upper surface of the 
main valve, it is convenient to begin in Fig. 3 by placing the 
port a in a convenient position near the exhaust-space e. 
From the right-hand edge of this port lay off f of an inch to c, 
the left-hand edge of the outer part of the cut-off valve ; this is 
equal to the greatest displacement of that valve, and insures 
that the edge c shall not overrun and contract the port a. 
From c lay off somewhat more than f of an inch, in this case 
if of an inch, to the left-hand edge of the port b ; this gives 
the necessary length of the bar cd in order that leakage may 
not occur past the edge c at the maximum displacement 



114 VALVE-GEARS FOR STEAM-ENGINES. 

toward the right. The clearance, f of an inch, is laid off from 
the right-hand edge of the port b^ to determine the edge d of 
the bar cd. The inner right-hand bar is made as wide as cd. 
The left-hand half of the main valve and cut-off valve is 
a counterpart of the right-hand half. 

The cut-off valve-spindle takes hold of a lug on one of the 
bars of the gridiron cut-off valve ; and the main valve-spindle 
passes through a tube or passage cored out through the middle 
of that valve. 

To Set a Double Valve-gear. — Set the main valve to 
give equal lead ; the cut-off by that valve has little influence 
on the running of the engine, and requires little or no atten- 
tion. If the cut-off valve is designed to cut off at a definite 
point when the engine is running under normal conditions, 
equalize the cut-off by that valve at that point. If the load on 
the engine and the cut-off are variable within a limited range, 
the valve should be set to give the least irregularity within that 
range ; it will usually be sufficient to equalize the cut-off for 
the middle of the range. If the range of cut-off is wide it will 
often be impossible to get a good action for the entire range, 
and then it will be advisable to equalize the cut-off for some 
early point in the stroke of the piston. It has already been 
pointed out that the Meyer valve may have the cut-off equal- 
ized at two points of the stroke by using unequal pitches for 
the screws on the valve-spindle. 



CHAPTER VI. 
DROP CUT-OFF VALVE-GEARS. 

In this chapter there will be given descriptions of a few- 
special forms of valve-gears, selected, partly at random, from 
the large variety of such gears employed by the builders of 
automatic cut-off stationary engines. All are of the four-valve 
type of valve-gears, and all give a drop or disengagement cut- 
off. A description and analysis of these few forms will enable 
the student to analyze and understand other gears of similar 
types. 

Brown Engine Gear. — Fig. i, PI. XXX, gives a section 
through the head-end valves and valve-chests of the Brown 
engine ; the crank-end valves and gears are a duplication of those 
for the head end. The admission-valve F is a five-ported 
gridiron valve on a vertical valve-seat, and the exhaust-valve 
is a three-ported gridiron valve on a horizontal seat. Both 
are controlled by valve-gears on the shaft O, which is driven 
by the engine-shaft through a pair of equal bevel-gears and 
makes one revolution for each revolution of the engine. It is 
clear that four such valves might be driven directly by one 
eccentric on the engine-shaft, or by four eccentrics on the shaft 
Oj and that in such case the four valves would be equivalent 
to one plain slide-valve, and would be designed by the princi- 
ples laid down in the first chapter. 

The eccentric E, which moves the steam valve-gear, is set 
to one side of a vertical through ^, so that it gives a rapid 

115 



Il6 VALVE-GEARS FOR STEAM-ENGINES. 

Upward motion to the lever />. The toe of the lever /> catches 
under the edge of the latch Z, and lifts the valve V through 
the spindle SV. When the tail of the latch strikes the pin dy 
the valve is disengaged from the lever />, and it falls shut ; 
a dash-pot P checks the motion of the valve and prevents jar. 
The pin d on the arm bd is under the control of the governor 
through the herizontal shaft b. It is commonly said that the 
governor on an engine with a detachment cut-off gear has only 
the light duty of setting the stop (in this case the pin d) that 
unlatches the gear and releases the valve ; the friction of the 
governor and the attached parts is, or should be, small. Most 
such gears throw a shock on the governor, tending to disturb 
it and make it race when the cut-off valve is released ; and the 
governor should be sufficiently powerful to resist the shock. 
In this gear, when the tail of the latch L strikes the pin d^ the 
shock tends to open the latch and to throw the pin toward the 
left ; both will yield, but the motion of d, and consequently of 
the governor, is slight. 

The exhaust-valve is moved by the cam C, which consists 
of a groove, in the face of a disk, in which works a roller on 
the end of the lever trS' , The end S' of the lever is slotted 
and provided with a block to avoid bending the valve-spindle 
V S' . The action of this cam is equivalent to that of an eccen- 
tric, except that there are periods of rest when the valve is 
open or shut. Fig. 2 shows two ways of laying out such a 
cam ; it is intended to show general principles only, and would 
require some modification to fit it to the engine shown by 
Fig. I. Let it be supposed that the cam acts directly on the 
end of a horizontal valve-spindle, such as V S' ^ Fig. i, and that 
its centre is on a prolongation of the path of the valve-spindle. 
Suppose further that the cam turns toward the left, and that 
the valve shall begin to open when the line Od is horizontal,, 
and be wide open when Ob is horizontal. To give a uniform 
motion to the cam, make the curve i, 3, 7 an arc of an Archi- 
medean spiral ; this is done by dividing the angular space Mand 



DROP CUT-OFF VALVE-GEARS. 11/ 

the linear space 1^7 into the same number of equal parts, and 
by drawing intersecting arcs and radii, 6'6, 6^6, 5^5, 6^5, etc., as 
shown. The cam from ^ to <: is a circular groove, so that the 
cam remains at rest till the line Oc comes into coincidence with 
the path of the valve-spindle. The groove from the line Oc to 
the line Oa is so designed that it gives a harmonic motion. 
On the line \'j a semicircle is drawn, and its arc and the 
angular space cOa are divided into the same number of equal 
parts; arcs and radii are drawn intersecting at i, 2, 3, etc. 
Finally, the cam from Oa to Od is a circular arc, giving a period 
of rest. The second construction, giving harmonic motion, is 
to be preferred for heavy valves having a rapid motion, in 
order that they may start and stop easily and quietly ; for 
valves that move slowly and have a large frictional resistance, 
the first construction may be preferable, but the cam should be 
modified by rounding the corners at i and 7, to avoid a shock 
at starting and stopping. The positions of the lines Ob, Od^ 
Oa, and Oc may be chosen by the designer so that the time 
and rate at which the valve opens and shuts may conform to 
the requirements of his design and to the dictates of his judg- 
ment and experience. 

The cam in the figure has a symmetry with regard to the 
axes xx' and yy' that suggests the resemblance of its action to 
that of an eccentric. 

It is neither necessary nor customary to balance valves of 
the type used on the Brown engine, for they have little press- 
ure on them to produce friction when they are moving, and 
when they are shut they are at rest. It is usual and advisable 
to set the exhaust-valve to give compression nearly up to the 
steam-pressure in the steam-chest, so that the pressure under 
the steam-valve is nearly equal to the pressure on it at admis- 
sion. The valve drops shut at cut-off, and after it is at rest 
the steam-pressure in the cylinder is reduced by expansion. 
The expansion is carried down to within a few pounds of the 
back-pressure, so that at release the pressure on the exhaust- 



Il8 VALVE-GEARS FOR STEAM-ENGINES. 

valve is not excessive ; at compression the pressure in the cyl- 
inder rises after the valve is at rest. 

A feature common to many detachment cut-off gears can 
be well shown by reference to Fig. i, PL XXX. Let it be 
supposed that the eccentric E has no angular advance, and 
that the valve has no lead ; then the valve will open at the be- 
ginning of the stroke, and will have its greatest displacement, 
provided that it is not sooner released, when the piston is at or 
near half-stroke. If the latch has not then struck the pin d, it 
will not strike it at all, and the valve will remain connected to 
the gear, and will close at or near the end of the stroke. It is 
also evident that giving angular advance to the eccentric and 
lap to the valve will limit still further the range of cut-off. In 
this gear, however, the cut-off may be continued beyond half- 
stroke by giving a negative angular advance to the eccentric 
and a clearance to the valve. If an engine with a detachment 
cut-off that is limited to the first half of the stroke is over- 
loaded, there is a liability that a failure to cut-off will occur, 
in which case the sudden increase of work due to the steam 
following the piston to the end of the stroke will make the en- 
gine run very irregularly. 

Corliss Valve-gear. — Of all types of detachment valve- 
gears, that invented by Corliss has been most widely known 
and has received the most favor. A modification of this gear 
designed by Mr. Edwin Reynolds is shown by Plate XXXI, 
which represents the valve-gear on the intermediate cylinder 
of the triple-expansion engine in the Engineering Laboratories 
of the Massachusetts Institute of Technology. 

The Corliss type of engine has two steam-chests, 5 for the 
supply and ^for the exhaust; the latter is separated from the 
cylinder in order that it may not be chilled by the exhaust 
steam. This arrangement produces a somewhat rectangular 
casting containing the steam-chests and the cylinder, at the 
four corners of which are placed four valves, two of which, 
V and V, are admission- or steam-valves, and the other two, W 



DROP CUT-OFF VALVE-GEARS, II9 

and Wj are exhaust-valves. The valve-seats are bored cylindri- 
cal and the faces of the valves are turned to fit ; the valves 
bear on half a circle or less, and are so connected to the valve- 
spindles that they may follow the valve-seats without cramping 
the valve-spindles. The valve-spindles, which are at right an- 
angles to the axis of the cylinder, project through stuffing- 
boxes and carry cranks on the ends, by means of which the 
valves are turned on their seats. The exhaust-valves IV and 
w have their valve-cranks WD and wd connected directly to 
pins A and a, in a wrist-plate Oy which receives a harmonic os- 
cillation from an eccentric on the engine-shaft. The admission- 
valves take steam on their inner edges as shown at v, and 
their cranks carry blocks as shown at the crank end. In the 
figure a section is taken just behind the crank Vh, which is 
represented by a dotted line only, in order to show the disen- 
gagement-latch zTh, which engages the block h and is carried 
by the bell-crank lever EVT\ the lever EVT is connected by 
the link EB to the wrist-plate. The latch is opened when the 
finger Tz strikes the stop x on the ring xr ; the ring is placed 
under the control of the governor through the cut-off rod NM 
and the double-armed bell-crank lever Mint, to which the gov- 
ernor-rod is attached at /. The linkage made up of the valve- 
crank, valve-rod, and wrist-plate, for example Oadw, is designed 
to give a slow motion when the valve is closed, and a rapid 
motion when opening or closing. The figure shows the wrist- 
plate and valves in mid-position, the eccentric being erect. 
The exhaust-valve w has its edge on the edge of the port ; its 
crank moves through the angle dwd^ , while the wrist-pin oscil- 
lates through the angle aOa^ , but that crank has only the an- 
gular motion dwd^ while the wrist-plate moves through the 
angle aOa^ = aOa^. The admission-valves have a similar ac- 
tion as shown at e^ve^. If it be supposed that the governor- 
balls are at their lowest position (at which the disengagement- 
gear does not act) it will be seen that this gear differs from the 
plain slide-valve gear in two points : first, it has four valves; 



I20 VALVE-GEARS FOR STEAM-ENGINES. 

and second, these valves have a more favorable action when 
opening and closing, on account of the linkages just described. 

From a pin at g in the crank Vh, a dash-pot rod represented 
by the line gi leads to a vacuum dash-pot shown by Fig. 2. 
This dash-pot has two pistons,/ and P\ the lower piston fits 
nicely in a closed cylinder from which air is excluded ; the upper 
piston works in a larger cylinder that is open to the atmos- 
phere through a series of orifices i, i^, and i^ and the pipe O. 
When the valve-crank Vh, Fig. i, is raised, it lifts the double 
piston Pp and a partial vacuum is formed under p, while air 
enters freely, through the orifices 2, i^ , i^ , to the annular 
space under the piston P. When the valve is disengaged, the 
weight of the dash-pot and the dash-pot rod, aided by the vacu- 
um under the piston /, closes the valve promptly ; while the 
air under the piston Tracts as a buffer and prevents a shock. 
The pipe O is provided with a hollow plug as shown, by aid of 
which the escape of air through the orifices i, i^ , and i^ may be 
regulated. 

A large number of detachment-gears have been devised 
and used by Corliss, and by others who have used this type of 
valve-gear. The one shown by Fig. i, PL XXXI, was invented 
by Mr. Reynolds and has the advantage that the latch mechan- 
ism is centred on the same axis as the cut-off stop; conse- 
quently the finger z always strikes the stop ;i;at the same angle, 
and the same force is required to disengage the cut-off valve. 
The block, when disengaged, slides along the plate y. On 
the return motion the plate y slides over the block till it can 
snap on to it, under the influence of the spring st. 

It is customary to give a small lap to the steam-valves ; 
consequently, as with a plain slide-valve, the eccentric has a 
small angular advance. With such an arrangement the eccen- 
tric-centre will be on the line of dead-points, and the valves will 
have their greatest displacement when the crank has moved 
through 90° less the angular advance, and before the piston is 
at half-stroke. If the detachment-gear has not been released 



r 



DROP CUT-OFF VALVE-GEARS. 121 

before the valve has received Its greatest displacement, the 
valve will not be disengaged at all, but will remain under the 
•control of the linkage connecting it to the wrist-plate ; and 
cut-off will occur near the end of the stroke, and will be deter- 
mined by the lap and angular advance as with a plain slide- 
valve. It is therefore evident that the range of cut-off for the 
ordinary form of the Corliss gear is from the beginning of the 
stroke to half-stroke or less. When a longer cut-off is desired, 
for example, on the low-pressure cylinder of a compound engine, 
two wrist-plates may be used : one wrist-plate, moved by an 
eccentric with a small angular advance, has control of the 
exhaust-valves, and gives release and compression near the 
ends of the stroke ; the other wrist-plate is moved by an 
eccentric with a negative angular advance, and has control of 
the steam-valves which have a clearance instead of a lap : with 
this device the range of cut-off may be extended beyond half- 
stroke. 

Expertness in laying out Corliss valve-gears can be obtained 
only by experience, with good examples for models. The 
steam-port may be made from J^- to -^-^ of the area of the pis- 
ton, and the exhaust-port may be made y^ to Jy of that area. 
The exhaust-valve commonly has no lap ; the admission-valve 
has a small lap, \ of an inch, in Fig. i, PI. XXXI. In that 
figure ve is the mid-position of the steam valve-crank, and e' e^ 
is the maximum valve-displacement, equal to the lap plus 
the port-opening ; ve, is the extreme position of the valve- 
crank. The points b and b^ are found by Intersecting the arc 
bj}^ by arcs drawn from e and e^ with a radius equal to the 
length of the link BE. The arc bb^ is made equal to bb^ , and 
ve^ , the extreme position of the crank when the valve is shut, 
is found by intersecting the arc e^e^ by an arc drawn from b.^ 
with a radius equal to the length of the link. The linkage 
Oadw is laid out in a similar way, except that the angle aOa^ 
is from necessity equal to bOb. The lengths of the valve-cranks 
and the radii from the centre of the wrist-plate to the pins a 



122 VALVE-GEARS FOR STEAM-ENGINES. 

and b depend partly on the proportions of the engine and 
partly on the habit and discretion of the designer; the longer 
they are the less will be the force exerted on the links, ad and 
be, and on the pins which they connect. The angle veb should 
be nearly a right angle, so that a rapid opening of the valve 
maybe obtained. The pin C in the wrist-plate receives motion 
from the eccentric either ' directly or through a carrier or 
single-armed rocker that magnifies the throw of the eccen- 
tric in about the proportion of i : ij. The chord of the 
arc C^C^j through which C swings, is not longer than the 
radius OC in order that the angle CfiC may not be more 
than 30°. The linkages Oadw and Obev are to be laid out by 
trial to give as nearly as may be the desired motion to the 
valves. It will be noticed that the radius Oa^ and the link a^d^ 
are in one straight line at the extreme position of the exhaust- 
valve ; and in like manner Ob^ and b^e^ are in one line ; should 
the linkages be carried beyond these positions, a double oscil- 
lation would be given to the valve-cranks, which is considered 
to have a bad appearance. The system of rods and levers 
connecting the rings xqN and vn with the governor is laid 
out so that the cut-off may come at the beginning of the stroke 
when the governor stands at the top of its range of motion, 
and when the governor is at the bottom of that range the cut- 
off may come at or after half-stroke, i.e. the valve will not be 
released. Though it is not always done, it will be advisable 
for an inexperienced designer to draw the valve-ellipse for the 
steam- and exhaust-valves. The ellipse, or more properly the 
oval, will have a form like that shown by Fig. 3. The valve 
will be found to open rapidly and to nearly its full width early 
in the stroke of the piston. A line nn' drawn at the distance 
xn, equal to the lap from the axis xx' , will show that the cut- 
off occurs near the end of the stroke. The valve will be found 
to be nearly at rest during the greater part of the time when 
it is closed. 

The steam-valve is disengaged when the latch holding it is 



DROP CUT-OFF VALVE-GEARS. I23 

released, but cut-off does not occur till the edge of the valve 
comes to the edge of the port, which is an appreciable time 
later. In Fig. 3, PI. XXXI, let a represent the point of dis- 
engagement ; then, under the influence of the dash-pot, the 
valve falls with an accelerated velocity till it is checked by the 
air-cushion in the dash-pot. Representing the motion of the 
piston by abscissae, and the motion of the valve by ordinates 
(just as in drawing the ellipse), the action of the valve in closing 
may be represented by the dotted line abc\ the point of cut- 
off is represented by b at the intersection of this line and the 
lap-line 7in' . The piston-displacements may be readily found 
from the dimensions of the engine and Its speed of rotation, 
but the forces acting on the valve and its resistances cannot 
be estimated. The forces are the weight of the dash-pot and 
attached parts, together with the pressure of the atmosphere 
on the area of the piston/. The resistances are friction of 
the valve, of the dash-pot, and of other parts of the mechan- 
ism, and the varying pressures under the pistons P and/; the 
pressure under P is due to the escaping air, and under/ to the 
air beneath it when at its lowest position. Though the line 
abc cannot be determined by calculation or construction, it 
may be found experimentally by an apparatus described on 
page 7 for making an engine draw its own ellipse. The 
action of the valves of a Corliss engine is commonly investi- 
gated by aid of a steam-engine indicator; if the indicator-dia- 
gram shows a sharp cut-off, and if the other features are good, 
the action of the valves is considered to be satisfactory. 

Putnam Valve-gear. — The Putnam engine has four double 
poppet-valves, two for admission and two for exhaust. Plate 
XXXII shows a section through one of the admission-valves, 
and its valve-gear. XX' is a casting bolted onto the cylinder- 
casting. The space SS' is the steam-chest, and the space P 
leads to the cylinder. The two valves V and F", are made of 
composition and, when closed, rest on composition seats let 
into the casting. The seat of the valve V is large enough to 



124 VALVE-GEARS FOR STEAM-ENGINES. 

pass the valve V^, so that the valves maybe readily withdrawn 
through the hand-hole H, The unbalanced pressure, which must 
be overcome when the valve is opened, is that on the excess 
of the area of the upper valve over that of the lower valve. 
The valve-spindle ab is made of iron to avoid unequal expan- 
sion and consequent leakage ; for, if the distance between the 
valves is not exactly the same as the distance between the 
valve-seats, one or other of the valves will not come properly 
to its seat. 

The valve-spindle ab is stepped into a frame mn^ shown 
in section. The arms ^ and gq form a bell-crank lever, one 
arm of which, under the influence of the spring Ik^ presses on 
the frame inn\ a pin/' is interposed to reduce friction. The 
other 3inn, g-f, of the bell-crank lever carries the cam-lever />, 
which acts on the frame mn through the interposed sliding- 
block d and the pin / ; this cam-lever is driven by the double 
cam C. This cam C, and three others, one for the other steam- 
valve and two for the exhaust-valves, are carried by a shaft 
which is parallel to the axis of the cylinder and which is 
driven from the engine-shaft through bevel-gears, so pro- 
portioned that the cam-shaft makes one turn for two revolu- 
tions of the engine. The figure shows the cam in contact 
with the cam-lever, and the valves on their seats ; the engine 
is consequently at admission. As the engine moves forward, 
the cam-shaft turns as shown by the arrow and raises the 
valves, giving admission of steam, till the cam slides past the 
corner j/ of the cam-lever ; the valve is then released and falls 
shut under the influence of the spring k/. The governor-rod 
>takes hold of the pin k at the end of the lever ^^. When the 
speed of the engine increases and the governor rises, the lever 
/ig is thrown down and the cam-lever e/ is pushed to the left, 
so that the cut-off comes earlier. No shock is thrown on the 
governor when the valve is released, but as the edge of the 
cam is rounded to avoid cutting the cam-lever, there is a 
tendency to disturb the governor which the governor must be 



DROP CUT-OFF VALVE-GEARS. 1 25 

able to resist. Should the valve fail to close for any reason, 
the other end of the cam will strike on i and close the valve 
before the engine makes a return stroke. 

The exhaust-cam is shown at A. At each end the cam is 
cylindrical, so that it holds the exhaust-valve open till near 
the end of the stroke. The exhaust cam-lever is not placed 
under the control of the governor, but can be set to give a 
fixed compression. 

Gaskill Valve-gear. — One of the steam-valves for the 
high-pressure cylinder of the Gaskill horizontal pumping- 
engine, and part of the valve-gear, are shown on Plate XXXIII. 
The valve is shown in section by Fig. 2, and the seat is shown 
in section and half-plan by Figs. 2 and 3. The valve is of the 
Cornish type and differs from the double poppet-valve only 
in detail. Like that valve it consists of two valves joined 
together, the inner valve being small enough to pass through 
the valve-seat of the outer or upper valve. The unbalanced 
pressure to be overcome when the valve is opened is that on 
the difference of areas of the two valves. When open, both 
valves give admission of steam. The valve-seat vS is bolted 
to the cylinder-casting, and a passage leads directly to the end 
of the cylinder. The valve is covered by a small cylindrical 
valve-chest ; there are two such chests, one at each end of the 
cylinder, supplied by a branched steam-pipe. 

The valve-gear is shown by Fig. i, in which E is an eccen- 
tric on a shaft parallel to the axis of the cylinder, and driven 
from the engine-shaft through equal bevel-gears, so that it 
makes one turn for each revolution of the engine. The eccen- 
tric-strap has the cut-off toe a at one end and a lug b at the 
other. From b the rod bC leads to one end of an equal armed 
lever, and the valve-spindle d is hung from the other arm ; 
the distance between the rod C and the valve-spindle is several 
times as far as shown in the figure. The lever ^7, centred at 
h, is under the control of the governor through the rod ki. 



126 VALVE-GEARS FOR STEAM-ENGINES. 

The eccentric and eccentric-strap with the lever il form a 
radial-detachment cut-off gear. 

Suppose first that the lever hi is thrown so far to the right 
that the toe a does not touch it ; then as the centre of the 
eccentric describes a circular path around the point Oy the 
point b^ of the line b^Ea will move on an arc that sensibly 
coincides with the axis XX' ^ and the point a^ will describe an 
oval a^a^a^ ; the valve meanwhile will remain shut. 

On the other hand, if the lever hi is supposed to be so far 
to the left that the toe a may remain always in contact with 
its curved end, and if by some means it is prevented from 
rising from that surface, then the point a will travel on a 
circular arc nearly coincident with the axis XX' , and the point 
b will describe the oval bjbj?^ ; such an action is of course im- 
possible when the gear is connected up, as the valve is on its 
seat when the point b is on the axis XX' and consequently b 
cannot rise above that axis. 

With the lever hi in the position shown in the figure, the 
toe a describes the oval a^a^a^ till it comes in contact with the 
curved surface at the end of the lever ; and then a slides along 
that surface, while the point b describes the arc hj?^^ and the 
valve is opened as shown by Fig. 2. When the toe comes to 
the edge of the surface /, it slips off and the valve is thrown 
shut by the action of a spring and dash-pot. The toe falls 
from a\.o a^, and the point b^ returns to b on the axis XX' , 

It is evident that this form of valve-gear can give a range 
of cut-off varying from the beginning to the end of the stroke, 
and that the release does not throw a shock on the governor. 
On the other hand, the sudden opening of the steam-valve 
when the toe a comes in contact with the lever hi throws a 
shock on the valve-gear that might be troublesome at any but 
the low speeds at which pumping-engines are commonly run. 



INDEX. 



Admission, 5 

Allen link-motion, 61 

Allen valve, 26 

Angular advance, 5 

Area of steam-pipe and steam-ports, 14 

Auxiliary valve-circle, 103 

Balanced valves, 27 
Bell-crank lever, 11 
Brown engine gear, 115 

Clearance, 5 

Compression, 6 

Corliss valve-gear, 118 

Crank and connecting-rod, 2 

Cut-off, 5 

" equalization of, 19 

Cut-off valve on back of main valve, 
102 
" " in separate chest, 97 

" '* with constant travel, in 

** " with shifting eccentric, 

100 

Dead-centre, to set engine on, 29 
Designing Meyer valve, 106 

" link-motions, 67 

Diagram, elliptical, 6 

" sinusoidal, 7 

" Zeuner's, 8 
Double-ported valve, 25 
Drop cut-off valve-gears, 115 
Double valves, 97 

'* '* auxiliary circle, 103 



Eccentric and eccentric-rod, 3 
Equalization of cut-off, 19, 22 
Events of the stroke, 5 
Exhaust-space, 4 
Expansion and compression, 11 

Gaskill valve-gear, 125 
Gooch link-motion, 53 

Hackworth valve-gear, 93 
Joy valve-gear, 93 

Lap, inside and outside, 4 

Lap and lead, for link-motion, 74 

Lead, 5, 16 

" of link-motions, 52 
Lead-angle, 16 

Link-arc, radius of, 42, 54, 67 
Link-motion, 39 

Allen, 61 
** analytical discussion, 43, 

54 
** designing, 67 
** for locomotives, 71 
" for marine engines, 68 
** Gooch, 53 
" lap and lead, 74 
** location of reverse-shaft, 

76 
" location of rocker, 75 

" saddle-pin, 75 
" modifications, 65 



127 



128 



INDEX. 



Link-motion, open and crossed rods, 

41, 54 
port-opening, 78 
skeleton model, 72 
slip, 78 

Stephenson, 39 
to set, 80 
Zeuner's diagram, 51, 58 

Link-pins, 65 

Loose eccentric, 33 

Marshall valve-gear, 91 
Meyer valve-gear, 104 

" " cut-off at inner edge, 

108 
" " designing, 106 

** *' for reversing en- 

gines, 109 
Model for link-motion, 72 

" modifications, 79 
** applications, 81 



<( i c 

(I i( 



Piston-valve, 24 
Port-opening, 78 
Ports, 4 

" area of, 14 
Putnam valve-gear, 123 

Radial valve-gears, 88 

Radius of link-arc, 42, 49, 54, 67 

Reduction of slip of link-motion, 69 

Release, 5 

Reverse-shaft for link-motion, 66, 76 

Rocker, 11 

" equalization of cut-off by, 22 
" location for link-motion, 75 

Saddle-pin, 66 • 
Shaft-governor, 35, 37 
Shifting-eccentric, constant lead, 37 
" " variable lead, 33 

Sinusoidal diagram, 7 



Skeleton model for link-motion, 72 
Slide-valve, i, 4 

'* " problems, 17 

** " 10 lay out, 20 
Slip of link-motion, 78 
" , reduction of, 69 
Steam-pipe, area of, 14 
Stephenson link motion, 39 
Stroke, events of, 5 

To set a double valve, 114 

" ** link-motion, 80 

" " slide-valve, 28 

" " an engine on a dead-point, 29 
Trick valve, 26 

Valve, Allen or Trick, 26 
'* balanced, 27 
" double-ported, 25 
*' piston, 24 
Valve-circle, auxiliary, 103 
Valve-ellipse, 6 

Valve-gear, Brown engine, 115 
" " cam, 116 

" Corliss, 118 
** " double, 97 
" *' drop cut-off, 115 
*' " Gaskill, 125 
" ** Hackvvorth, 93 
" Joy, 93 
" Marshall, 88 
" *• Meyer, 104 
" " Putnam, 123 
" radial, 88 
" Walschaert, 88 
Valve-setting, for double valves, 114 
'* " for link-motions, 80 

'* ** for slide-valve, 28 

Walschaert gear, 88 

Zeuner's diagram, 8, 51, 58 




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